algebra 8-1studyguide
TRANSCRIPT
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks in both English and Spanish.
Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7
ANSWERS FOR WORKBOOKS The answers for Chapter 8 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-827732-9 Algebra 1Chapter 8 Resource Masters
2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03
Glencoe/McGraw-Hill
© Glencoe/McGraw-Hill iii Glencoe Algebra 1
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 8-1Study Guide and Intervention . . . . . . . . 455–456Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 457Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 458Reading to Learn Mathematics . . . . . . . . . . 459Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 460
Lesson 8-2Study Guide and Intervention . . . . . . . . 461–462Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 463Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 464Reading to Learn Mathematics . . . . . . . . . . 465Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 466
Lesson 8-3Study Guide and Intervention . . . . . . . . 467–468Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 469Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 470Reading to Learn Mathematics . . . . . . . . . . 471Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 472
Lesson 8-4Study Guide and Intervention . . . . . . . . 473–474Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 475Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 476Reading to Learn Mathematics . . . . . . . . . . 477Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 478
Lesson 8-5Study Guide and Intervention . . . . . . . 479–480Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 481Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 482Reading to Learn Mathematics . . . . . . . . . . 483Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 484
Lesson 8-6Study Guide and Intervention . . . . . . . . 485–486Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 487Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 488Reading to Learn Mathematics . . . . . . . . . . 489Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 490
Lesson 8-7Study Guide and Intervention . . . . . . . . 491–492Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 493Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 494Reading to Learn Mathematics . . . . . . . . . . 495Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 496
Lesson 8-8Study Guide and Intervention . . . . . . . . 497–498Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 499Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 500Reading to Learn Mathematics . . . . . . . . . . 501Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 502
Chapter 8 AssessmentChapter 8 Test, Form 1 . . . . . . . . . . . . 503–504Chapter 8 Test, Form 2A . . . . . . . . . . . 505–506Chapter 8 Test, Form 2B . . . . . . . . . . . 507–508Chapter 8 Test, Form 2C . . . . . . . . . . . 509–510Chapter 8 Test, Form 2D . . . . . . . . . . . 511–512Chapter 8 Test, Form 3 . . . . . . . . . . . . 513–514Chapter 8 Open-Ended Assessment . . . . . . 515Chapter 8 Vocabulary Test/Review . . . . . . . 516Chapter 8 Quizzes 1 & 2 . . . . . . . . . . . . . . . 517Chapter 8 Quizzes 3 & 4 . . . . . . . . . . . . . . . 518Chapter 8 Mid-Chapter Test . . . . . . . . . . . . 519Chapter 8 Cumulative Review . . . . . . . . . . . 520Chapter 8 Standardized Test Practice . . 521–522
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A35
© Glencoe/McGraw-Hill iv Glencoe Algebra 1
Teacher’s Guide to Using theChapter 8 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 8 Resource Masters includes the core materials neededfor Chapter 8. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 8-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Algebra 1
Assessment OptionsThe assessment masters in the Chapter 8Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 470–471. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
88
© Glencoe/McGraw-Hill vii Glencoe Algebra 1
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 8.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
binomial
by·NOH·mee·uhl
constant
degree of a monomial
degree of a polynomial
FOIL method
monomial
mah·NOH·mee·uhl
negative exponent
polynomial
PAH·luh·NOH·mee·uhl
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Algebra 1
Vocabulary Term Found on Page Definition/Description/Example
Power of a Power
Power of a Product
Product of Powers
Power of a Quotient
Quotient of Powers
scientific notation
trinomial
try·NOH·mee·uhl
zero exponent
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
88
Study Guide and InterventionMultiplying Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
6-18-1
© Glencoe/McGraw-Hill 455 Glencoe Algebra 1
Less
on
8-1
Multiply Monomials A monomial is a number, a variable, or a product of a numberand one or more variables. An expression of the form xn is called a power and representsthe product you obtain when x is used as a factor n times. To multiply two powers that havethe same base, add the exponents.
Product of Powers For any number a and all integers m and n, am � an � am � n.
Simplify (3x6)(5x2).
(3x6)(5x2) � (3)(5)(x6 � x2) Associative Property
� (3 � 5)(x6 � 2) Product of Powers
� 15x8 Simplify.
The product is 15x8.
Simplify (�4a3b)(3a2b5).
(�4a3b)(3a2b5) � (�4)(3)(a3 � a2)(b � b5)� �12(a3 � 2)(b1 � 5)� �12a5b6
The product is �12a5b6.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Simplify.
1. y( y5) 2. n2 � n7 3. (�7x2)(x4)
4. x(x2)(x4) 5. m � m5 6. (�x3)(�x4)
7. (2a2)(8a) 8. (rs)(rs3)(s2) 9. (x2y)(4xy3)
10. (2a3b)(6b3) 11. (�4x3)(�5x7) 12. (�3j2k4)(2jk6)
13. (5a2bc3)� abc4� 14. (�5xy)(4x2)( y4) 15. (10x3yz2)(�2xy5z)1�5
1�3
© Glencoe/McGraw-Hill 456 Glencoe Algebra 1
Powers of Monomials An expression of the form (xm)n is called a power of a powerand represents the product you obtain when xm is used as a factor n times. To find thepower of a power, multiply exponents.
Power of a Power For any number a and all integers m and n, (am)n � amn.
Power of a Product For any number a and all integers m and n, (ab)m � ambm.
Simplify (�2ab2)3(a2)4.
(�2ab2)3(a2)4 � (�2ab2)3(a8) Power of a Power
� (�2)3(a3)(b2)3(a8) Power of a Product
� (�2)3(a3)(a8)(b2)3 Commutative Property
� (�2)3(a11)(b2)3 Product of Powers
� �8a11b6 Power of a Power
The product is �8a11b6.
Simplify.
1. (y5)2 2. (n7)4 3. (x2)5(x3)
4. �3(ab4)3 5. (�3ab4)3 6. (4x2b)3
7. (4a2)2(b3) 8. (4x)2(b3) 9. (x2y4)5
10. (2a3b2)(b3)2 11. (�4xy)3(�2x2)3 12. (�3j2k3)2(2j2k)3
13. (25a2b)3� abc�214. (2xy)2(�3x2)(4y4) 15. (2x3y2z2)3(x2z)4
16. (�2n6y5)(�6n3y2)(ny)3 17. (�3a3n4)(�3a3n)4 18. �3(2x)4(4x5y)2
1�5
Study Guide and Intervention (continued)
Multiplying Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-18-1
ExampleExample
ExercisesExercises
Skills PracticeMultiplying Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-18-1
© Glencoe/McGraw-Hill 457 Glencoe Algebra 1
Less
on
8-1
Determine whether each expression is a monomial. Write yes or no. Explain.
1. 11
2. a � b
3.
4. y
5. j3k
6. 2a � 3b
Simplify.
7. a2(a3)(a6) 8. x(x2)(x7)
9. (y2z)(yz2) 10. (�2k2)(�3k)
11. (e2f4)(e2f 2) 12. (cd2)(c3d2)
13. (2x2)(3x5) 14. (5a7)(4a2)
15. (4xy3)(3x3y5) 16. (7a5b2)(a2b3)
17. (�5m3)(3m8) 18. (�2c4d)(�4cd)
19. (102)3 20. (p3)12
21. (�6p)2 22. (�3y)3
23. (3pq2)2 24. (2b3c4)2
GEOMETRY Express the area of each figure as a monomial.
25. 26. 27.
4p
9p3cd
cdx2
x5
p2�q2
© Glencoe/McGraw-Hill 458 Glencoe Algebra 1
Determine whether each expression is a monomial. Write yes or no. Explain.
1.
2.
Simplify.
3. (�5x2y)(3x4) 4. (2ab2c2)(4a3b2c2)
5. (3cd4)(�2c2) 6. (4g3h)(�2g5)
7. (�15xy4)�� xy3� 8. (�xy)3(xz)
9. (�18m2n)2�� mn2� 10. (0.2a2b3)2
11. � p�212. � cd3�2
13. (0.4k3)3 14. [(42)2]2
GEOMETRY Express the area of each figure as a monomial.
15. 16. 17.
GEOMETRY Express the volume of each solid as a monomial.
18. 19. 20.
21. COUNTING A panel of four light switches can be set in 24 ways. A panel of five lightswitches can set in twice this many ways. In how many ways can five light switches be set?
22. HOBBIES Tawa wants to increase her rock collection by a power of three this year andthen increase it again by a power of two next year. If she has 2 rocks now, how manyrocks will she have after the second year?
7g2
3g
m3nmn3
n
3h23h2
3h2
6ac3
4a2c
5x3
6a2b4
3ab2
1�4
2�3
1�6
1�3
b3c2�2
21a2�7b
Practice Multiplying Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-18-1
Reading to Learn MathematicsMultiplying Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-18-1
© Glencoe/McGraw-Hill 459 Glencoe Algebra 1
Less
on
8-1
Pre-Activity Why does doubling speed quadruple braking distance?
Read the introduction to Lesson 8-1 at the top of page 410 in your textbook.
Find two examples in the table to verify the statement that when speed isdoubled, the braking distance is quadrupled. Write your examples in thetable.
Speed Braking Distance Speed Doubled Braking Distance (miles per hour) (feet) (miles per hour) Quadrupled (feet)
Reading the Lesson
1. Describe the expression 3xy using the terms monomial, constant, variable, and product.
2. Complete the chart by choosing the property that can be used to simplify eachexpression. Then simplify the expression.
Expression Property Expression Simplified
Product of Powers
35 � 32 Power of a Power
Power of a Product
Product of Powers
(a3)4 Power of a Power
Power of a Product
Product of Powers
(�4xy)5 Power of a Power
Power of a Product
Helping You Remember
3. Write an example of each of the three properties of powers discussed in this lesson.Then, using the examples, explain how the property is used to simplify them.
© Glencoe/McGraw-Hill 460 Glencoe Algebra 1
An Wang An Wang (1920–1990) was an Asian-American who became one of thepioneers of the computer industry in the United States. He grew up inShanghai, China, but came to the United States to further his studiesin science. In 1948, he invented a magnetic pulse controlling devicethat vastly increased the storage capacity of computers. He laterfounded his own company, Wang Laboratories, and became a leader inthe development of desktop calculators and word processing systems.In 1988, Wang was elected to the National Inventors Hall of Fame.
Digital computers store information as numbers. Because theelectronic circuits of a computer can exist in only one of two states,open or closed, the numbers that are stored can consist of only twodigits, 0 or 1. Numbers written using only these two digits are calledbinary numbers. To find the decimal value of a binary number, youuse the digits to write a polynomial in 2. For instance, this is how tofind the decimal value of the number 10011012. (The subscript 2 indicates that this is a binary number.)
10011012 � 1 � 2�
6�
� 0 � 2�
5�
� 0 � 2�
4�
� 1 � 2�
3�
� 1 � 2�
2�
� 0 � 2�
1�
� 1 � 2�
0�
� 1 � 6�4�
� 0 � 3�2�
� 0 � 1�6�
� 1 � 8�
� 1 � 4�
� 0 � 2�
� 1 � 1�
� 64 � 0 � 0 � 8 � 4 � 0 � 1
� 77
Find the decimal value of each binary number.
1. 11112 2. 100002 3. 110000112 4. 101110012
Write each decimal number as a binary number.
5. 8 6. 11 7. 29 8. 117
9. The chart at the right shows a set of decimal code numbers that is used widely in storing letters of the alphabet in a computer's memory.Find the code numbers for the letters of your name. Then write the code for your name using binary numbers.
The American Standard Guide for Information Interchange (ASCII)
A 65 N 78 a 97 n 110B 66 O 79 b 98 o 111C 67 P 80 c 99 p 112D 68 Q 81 d 100 q 113E 69 R 82 e 101 r 114F 70 S 83 f 102 s 115G 71 T 84 g 103 t 116H 72 U 85 h 104 u 117I 73 V 86 i 105 v 118J 74 W 87 j 106 w 119K 75 X 88 k 107 x 120L 76 Y 89 l 108 y 121M 77 Z 90 m 109 z 122
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
8-18-1
Study Guide and InterventionDividing Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
6-28-2
© Glencoe/McGraw-Hill 461 Glencoe Algebra 1
Less
on
8-2
Quotients of Monomials To divide two powers with the same base, subtract theexponents.
Quotient of Powers For all integers m and n and any nonzero number a, � am � n.
Power of a Quotient For any integer m and any real numbers a and b, b � 0, � �m� .am
�bm
a�b
am�an
Simplify . Assume
neither a nor b is equal to zero.
� � �� � Group powers with the same base.
� (a4 � 1)(b7 � 2) Quotient of Powers
� a3b5 Simplify.
The quotient is a3b5 .
b7�b2
a4�a
a4b7�ab2
a4b7�ab2 Simplify � �3
.
Assume that b is not equal to zero.
� �3� Power of a Quotient
� Power of a Product
� Power of a Power
� Quotient of Powers
The quotient is .8a9b9�27
8a9b9�27
8a9b15�27b6
23(a3)3(b5)3��
(3)3(b2)3
(2a3b5)3�
(3b2)32a3b5�
3b2
2a3b5�
3b2Example 1Example 1 Example 2Example 2
ExercisesExercises
Simplify. Assume that no denominator is equal to zero.
1. 2. 3.
4. 5. 6.
7. 8. � �39. � �3
10. � �411. � �4
12. r7s7t2�s3r3t2
3r6s3�2r5s
2v5w3�v4w3
4p4q4�3p2q2
2a2b�a
xy6�y4x
�2y7�14y5
x5y3�x5y2
a2�a
p5n4�p2n
m6�m4
55�52
© Glencoe/McGraw-Hill 462 Glencoe Algebra 1
Negative Exponents Any nonzero number raised to the zero power is 1; for example,(�0.5)0 � 1. Any nonzero number raised to a negative power is equal to the reciprocal of the number raised to the opposite power; for example, 6�3 � . These definitions can be used to simplify expressions that have negative exponents.
Zero Exponent For any nonzero number a, a0 � 1.
Negative Exponent Property For any nonzero number a and any integer n, a�n � and � an.
The simplified form of an expression containing negative exponents must contain onlypositive exponents.
Simplify . Assume that the denominator is not equal to zero.
� � �� �� �� � Group powers with the same base.
� (a�3 � 2)(b6 � 6)(c5) Quotient of Powers and Negative Exponent Properties
� a�5b0c5 Simplify.
� � �(1)c5 Negative Exponent and Zero Exponent Properties
� Simplify.
The solution is .
Simplify. Assume that no denominator is equal to zero.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. � �0 12.(�2mn2)�3��
4m�6n44m2n2�8m�1�
s�3t�5�(s2t3)�1
(3st)2u�4��s�1t2u7
(6a�1b)2��
(b2)4
x4y0�x�2
(a2b3)2�(ab)�2
(�x�1y)0��4w�1y2
b�4�b�5
p�8�p3
m�m�4
22�2�3
c5�4a5
c5�4a5
1�a5
1�4
1�4
1�4
1�c�5
b6�b6
a�3�a2
4�16
4a�3b6��16a2b6c�5
4a�3b6��16a2b6c�5
1�a�n
1�an
1�63
Study Guide and Intervention (continued)
Dividing Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-28-2
ExampleExample
ExercisesExercises
Skills PracticeDividing Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-28-2
© Glencoe/McGraw-Hill 463 Glencoe Algebra 1
Less
on
8-2
Simplify. Assume that no denominator is equal to zero.
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12.
13. � �214. 4�4
15. 8�2 16. � ��2
17. � ��118.
19. k0(k4)(k�6) 20. k�1(��6)(m3)
21. 22. � �0
23. 24.
25. 26. 48x6y7z5���6xy5z6
�15w0u�1��
5u3
15x6y�9�5xy�11
f�5g4�h�2
16p5q2�2p3q3
f�7�f4
h3�h�6
9�11
5�3
4p7�7s2
32x3y2z5���8xyz2
�21w5u2��
7w4u5
m7n2�m3n2
a3b5�ab2
w4u3�w4u
12n5�36n
9d7�3d6
m�m3
r3s2�r3s4
x4�x2
912�98
65�64
© Glencoe/McGraw-Hill 464 Glencoe Algebra 1
Simplify. Assume that no denominator is equal to zero.
1. 2. 3.
4. 5. 6.
7. � �38. � �2
9.
10. x3( y�5)(x�8) 11. p(q�2)(r�3) 12. 12�2
13. � ��214. � ��4
15.
16. 17. 18. � �0
19. 20. 21.
22. 23. 24.
25. � ��526. � ��1
27. � ��2
28. BIOLOGY A lab technician draws a sample of blood. A cubic millimeter of the bloodcontains 223 white blood cells and 225 red blood cells. What is the ratio of white bloodcells to red blood cells?
29. COUNTING The number of three-letter “words” that can be formed with the Englishalphabet is 263. The number of five-letter “words” that can be formed is 265. How manytimes more five-letter “words” can be formed than three-letter “words”?
2x3y2z�3x4yz�2
7c�3d3�c5de�4
q�1r3�qr�2
(2a�2b)�3��
5a2b4( j�1k3)�4�
j3k3
m�2n�5��(m4n3)�1
r4�(3r)3
�12t�1u5v�4��
2t�3uv56f�2g3h5��54f�2g�5h3
x�3y5�4�3
8c3d2f4��4c�1d2f�3
�15w0u�1��
5u3
22r3s2�11r2s�3
4�3
3�7
�4c2�24c5
6w5�7p6s3
4f 3g�3h6
8y7z6�4y6z5
5c2d3��4c2d
m5np�m4p
xy2�xy
a4b6�ab3
88�84
Practice Dividing Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-28-2
Reading to Learn MathematicsDividing Monomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-28-2
© Glencoe/McGraw-Hill 465 Glencoe Algebra 1
Less
on
8-2
Pre-Activity How can you compare pH levels?
Read the introduction to Lesson 8-2 at the top of page 417 in your textbook.
• In the formula c � � �pH, identify the base and the exponent.
• How do you think c will change as the exponent increases?
Reading the Lesson
1. Explain what the statement � am � n means.
2. To find c in the formula c � � �pH, you can find the power of the numerator, the power of
the denominator, and divide. This is an example of what property?
3. Use the Quotient of Powers Property to explain why 30 � 1.
4. Consider the expression 4�3.
a. Explain why the expression 4�3 is not simplified.
b. Define the term reciprocal.
c. 4�3 is the reciprocal of what power of 4?
d. What is the simplified form of 4�3?
Helping You Remember
5. Describe how you would help a friend who needs to simplify the expression .4x2�2x5
1�10
am�an
1�10
© Glencoe/McGraw-Hill 466 Glencoe Algebra 1
Patterns with PowersUse your calculator, if necessary, to complete each pattern.
a. 210 � b. 510 � c. 410 �
29 � 59 � 49 �
28 � 58 � 48 �
27 � 57 � 47 �
26 � 56 � 46 �
25 � 55 � 45 �
24 � 54 � 44 �
23 � 53 � 43 �
22 � 52 � 42 �
21 � 51 � 41 �
Study the patterns for a, b, and c above. Then answer the questions.
1. Describe the pattern of the exponents from the top of each column to the bottom.
2. Describe the pattern of the powers from the top of the column to the bottom.
3. What would you expect the following powers to be?20 50 40
4. Refer to Exercise 3. Write a rule. Test it on patterns that you obtain using 22, 25, and 24as bases.
Study the pattern below. Then answer the questions.
03 � 0 02 � 0 01 � 0 00 � 0�1 does not exist. 0�2 does not exist. 0�3 does not exist.
5. Why do 0�1, 0�2, and 0�3 not exist?
6. Based upon the pattern, can you determine whether 00 exists?
7. The symbol 00 is called an indeterminate, which means that it has no unique value.Thus it does not exist as a unique real number. Why do you think that 00 cannot equal 1?
?
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
8-28-2
Study Guide and InterventionScientific Notation
NAME ______________________________________________ DATE ____________ PERIOD _____
6-38-3
© Glencoe/McGraw-Hill 467 Glencoe Algebra 1
Less
on
8-3
Scientific Notation Keeping track of place value in very large or very small numberswritten in standard form may be difficult. It is more efficient to write such numbers inscientific notation. A number is expressed in scientific notation when it is written as aproduct of two factors, one factor that is greater than or equal to 1 and less than 10 and onefactor that is a power of ten.
Scientific NotationA number is in scientific notation when it is in the form a � 10n, where 1 � a � 10 and n is an integer.
Express 3.52 � 104 instandard notation.
3.52 � 104 � 3.52 � 10,000� 35,200
The decimal point moved 4 places to theright.
Express 37,600,000 inscientific notation.
37,600,000 � 3.76 � 107
The decimal point moved 7 places so that itis between the 3 and the 7. Since 37,600,000 � 1, the exponent is positive.
Express 6.21 � 10�5 instandard notation.
6.21 � 10�5 � 6.21 �
� 6.21 � 0.00001� 0.0000621
The decimal point moved 5 places to the left.
Express 0.0000549 inscientific notation.
0.0000549 � 5.49 � 10�5
The decimal point moved 5 places so that itis between the 5 and the 4. Since 0.0000549 � 1, the exponent is negative.
1�105
Example 1Example 1 Example 2Example 2
Example 3Example 3 Example 4Example 4
ExercisesExercises
Express each number in standard notation.
1. 3.65 � 105 2. 7.02 � 10�4 3. 8.003 � 108
4. 7.451 � 106 5. 5.91 � 100 6. 7.99 � 10�1
7. 8.9354 � 1010 8. 8.1 � 10�9 9. 4 � 1015
Express each number in scientific notation.
10. 0.0000456 11. 0.00001 12. 590,000,000
13. 0.00000000012 14. 0.000080436 15. 0.03621
16. 433 � 104 17. 0.0042 � 10�3 18. 50,000,000,000
© Glencoe/McGraw-Hill 468 Glencoe Algebra 1
Products and Quotients with Scientific Notation You can use properties ofpowers to compute with numbers written in scientific notation.
Evaluate (6.7 � 103)(2 � 10�5). Express the result in scientific andstandard notation.
(6.7 � 103)(2 � 10�5) � (6.7 � 2)(103 � 10�5) Associative Property
� 13.4 � 10�2 Product of Powers
� (1.34 � 101) � 10�2 13.4 � 1.34 � 101
� 1.34 � (101 � 10�2) Associative Property
� 1.34 � 10�1 or 0.134 Product of Powers
The solution is 1.34 � 10�1 or 0.134.
Evaluate . Express the result in scientific and
standard notation.
� � �� � Associative Property
� 0.368 � 103 Quotient of Powers
� (3.68 � 10�1) � 103 0.368 � 3.68 � 10�1
� 3.68 � (10�1 � 103) Associative Property
� 3.68 � 102 or 368 Product of Powers
The solution is 3.68 � 102 or 368.
Evaluate. Express each result in scientific and standard notation.
1. 2. 3. (3.2 � 10�2)(2.0 � 102)
4. 5. (7.7 � 105)(2.1 � 102) 6.
7. (3.3 � 105)(1.5 � 10�4) 8. 9.
10. FUEL CONSUMPTION North America burned 4.5 � 1016 BTU of petroleum in 1998.At this rate, how many BTU’s will be burned in 9 years? Source: The New York Times 2001 Almanac
11. OIL PRODUCTION If the United States produced 6.25 � 109 barrels of crude oil in1998, and Canada produced 1.98 � 109 barrels, what is the quotient of their productionrates? Write a statement using this quotient. Source: The New York Times 2001 Almanac
4 � 10�4��2.5 � 102
3.3 � 10�12��1.1 � 10�14
9.72 � 108��7.2 � 1010
1.2672 � 10�8��
2.4 � 10�12
3 � 10�12��2 � 10�15
1.4 � 104��2 � 102
108�105
1.5088�4.1
1.5088 � 108��4.1 � 105
1.5088 � 108��
4.1 � 105
Study Guide and Intervention (continued)
Scientific Notation
NAME ______________________________________________ DATE ____________ PERIOD _____
8-38-3
Example 1Example 1
Example 2Example 2
ExercisesExercises
Skills PracticeScientific Notation
NAME ______________________________________________ DATE ____________ PERIOD _____
8-38-3
© Glencoe/McGraw-Hill 469 Glencoe Algebra 1
Less
on
8-3
Express each number in standard notation.
1. 4 � 103 2. 2 � 108 3. 3.2 � 105
4. 3 � 10�6 5. 9 � 10�2 6. 4.7 � 10�7
ASTRONOMY Express the number in each statement in standard notation.
7. The diameter of Jupiter is 1.42984 � 105 kilometers.
8. The surface density of the main ring around Jupiter is 5 � 10�6 grams per centimetersquared.
9. The minimum distance from Mars to Earth is 5.45 � 107 kilometers.
Express each number in scientific notation.
10. 41,000,000 11. 65,100 12. 283,000,000
13. 264,701 14. 0.019 15. 0.000007
16. 0.000010035 17. 264.9 18. 150 � 102
Evaluate. Express each result in scientific and standard notation.
19. (3.1 � 107)(2 � 10�5) 20. (5 � 10�2)(1.4 � 10�4)
21. (3 � 103)(4.2 � 10�1) 22. (3 � 10�2)(5.2 � 109)
23. (2.4 � 102)(4 � 10�10) 24. (1.5 � 10�4)(7 � 10�5)
25. 26.7.2 � 10�5��4 � 10�3
5.1 � 106��1.5 � 102
© Glencoe/McGraw-Hill 470 Glencoe Algebra 1
Express each number in standard notation.
1. 7.3 � 107 2. 2.9 � 103 3. 9.821 � 1012
4. 3.54 � 10�1 5. 7.3642 � 104 6. 4.268 � 10�6
PHYSICS Express the number in each statement in standard notation.
7. An electron has a negative charge of 1.6 � 10�19 Coulomb.
8. In the middle layer of the sun’s atmosphere, called the chromosphere, the temperatureaverages 2.78 � 104 degrees Celsius.
Express each number in scientific notation.
9. 915,600,000,000 10. 6387 11. 845,320 12. 0.00000000814
13. 0.00009621 14. 0.003157 15. 30,620 16. 0.0000000000112
17. 56 � 107 18. 4740 � 105 19. 0.076 � 10�3 20. 0.0057 � 103
Evaluate. Express each result in scientific and standard notation.
21. (5 � 10�2)(2.3 � 1012) 22. (2.5 � 10�3)(6 � 1015)
23. (3.9 � 103)(4.2 � 10�11) 24. (4.6 � 10�4)(3.1 � 10�1)
25. 26. 27.
28. 29. 30.
31. BIOLOGY A cubic millimeter of human blood contains about 5 � 106 red blood cells. Anadult human body may contain about 5 � 106 cubic millimeters of blood. About how manyred blood cells does such a human body contain?
32. POPULATION The population of Arizona is about 4.778 � 106 people. The land area isabout 1.14 � 105 square miles. What is the population density per square mile?
2.015 � 10�3��
3.1 � 102
1.68 � 104��8.4 � 10�4
1.82 � 105��9.1 � 107
1.17 � 102��5 � 10�1
6.72 � 103��4.2 � 108
3.12 � 103��1.56 � 10�3
Practice Scientific Notation
NAME ______________________________________________ DATE ____________ PERIOD _____
8-38-3
Reading to Learn MathematicsScientific Notation
NAME ______________________________________________ DATE ____________ PERIOD _____
8-38-3
© Glencoe/McGraw-Hill 471 Glencoe Algebra 1
Less
on
8-3
Pre-Activity Why is scientific notation important in astronomy?
Read the introduction to Lesson 8-3 at the top of page 425 in your textbook.
In the table, each mass is written as the product of a number and a powerof 10. Look at the first factor in each product. How are these factors alike?
Reading the Lesson
1. Is the number 0.0543 � 104 in scientific notation? Explain.
2. Complete each sentence to change from scientific notation to standard notation.
a. To express 3.64 � 106 in standard notation, move the decimal point
places to the .
b. To express 7.825 � 10�3 in standard notation, move the decimal point
places to the .
3. Complete each sentence to change from standard notation to scientific notation.
a. To express 0.0007865 in scientific notation, move the decimal point places
to the right and write .
b. To express 54,000,000,000 in scientific notation, move the decimal point
places to the left and write .
4. Write positive or negative to complete each sentence.
a. powers of 10 are used to express very large numbers in
scientific notation.
b. powers of 10 are used to express very small numbers in
scientific notation.
Helping You Remember
5. Describe the method you would use to estimate how many times greater the mass ofSaturn is than the mass of Pluto.
© Glencoe/McGraw-Hill 472 Glencoe Algebra 1
Converting Metric UnitsScientific notation is convenient to use for unit conversions in the metric system.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
8-38-3
How many kilometersare there in 4,300,000 meters?
Divide the measure by the number ofmeters (1000) in one kilometer. Expressboth numbers in scientific notation.
� 4.3 � 103
The answer is 4.3 3 103 km.
4.3 � 106��1 � 103
Convert 3700 grams intomilligrams.
Multiply by the number of milligrams(1000) in 1 gram.
(3.7 � 103)(1 � 103) � 3.7 � 106
There are 3.7 � 106 mg in 3700 g.
Example 1Example 1 Example 2Example 2
Complete the following. Express each answer in scientific notation.
1. 250,000 m � km 2. 375 km � m
3. 247 m � cm 4. 5000 m � mm
5. 0.0004 km � m 6. 0.01 mm � m
7. 6000 m � mm 8. 340 cm � km
9. 52,000 mg � g 10. 420 kL � L
Solve.
11. The planet Mars has a diameter of 6.76 � 103 km. What is thediameter of Mars in meters? Express the answer in both scientificand decimal notation.
12. The distance from earth to the sun is 149,590,000 km. Lighttravels 3.0 � 108 meters per second. How long does it take lightfrom the sun to reach the earth in minutes? Round to the nearest hundredth.
13. A light-year is the distance that light travels in one year. (SeeExercise 12.) How far is a light year in kilometers? Express youranswer in scientific notation. Round to the nearest hundredth.
Study Guide and InterventionPolynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
6-48-4
© Glencoe/McGraw-Hill 473 Glencoe Algebra 1
Less
on
8-4
Degree of a Polynomial A polynomial is a monomial or a sum of monomials. Abinomial is the sum of two monomials, and a trinomial is the sum of three monomials.Polynomials with more than three terms have no special name. The degree of a monomialis the sum of the exponents of all its variables. The degree of the polynomial is the sameas the degree of the monomial term with the highest degree.
State whether each expression is a polynomial. If the expression isa polynomial, identify it as a monomial, binomial, or trinomial. Then give thedegree of the polynomial.
Expression Polynomial?Monomial, Binomial, Degree of the
or Trinomial? Polynomial
3x � 7xyzYes. 3x � 7xyz � 3x (�7xyz),
binomial 3which is the sum of two monomials
�25 Yes. �25 is a real number. monomial 0
7n3 3n�4No. 3n�4 � , which is not
none of these —a monomial
Yes. The expression simplifies to9x3 4x x 4 2x 9x3 7x 4, which is the sum trinomial 3
of three monomials
State whether each expression is a polynomial. If the expression is a polynomial,identify it as a monomial, binomial, or trinomial.
1. 36 2. 5
3. 7x � x 5 4. 8g2h � 7gh 2
5. 5y � 8 6. 6x x2
Find the degree of each polynomial.
7. 4x2y3z 8. �2abc 9. 15m
10. s 5t 11. 22 12. 18x2 4yz � 10y
13. x4 � 6x2 � 2x3 � 10 14. 2x3y2 � 4xy3 15. �2r8s4 7r2s � 4r7s6
16. 9x2 yz8 17. 8b bc5 18. 4x4y � 8zx2 2x5
19. 4x2 � 1 20. 9abc bc � d5 21. h3m 6h4m2 � 7
1�4y2
3�q2
3�n4
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 474 Glencoe Algebra 1
Write Polynomials in Order The terms of a polynomial are usually arranged so that the powers of one variable are in ascending (increasing) order or descending(decreasing) order.
Study Guide and Intervention (continued)
Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-48-4
Arrange the terms ofeach polynomial so that the powers ofx are in ascending order.
a. x4 � x2 � 5x3
�x2 5x3 x4
b. 8x3y � y2 � 6x2y � xy2
�y2 xy2 6x2y 8x3y
Arrange the terms ofeach polynomial so that the powers ofx are in descending order.
a. x4 � 4x5 � x2
4x5 x4 � x2
b. �6xy � y3 � x2y2 � x4y2
x4y2 � x2y2 � 6xy y3
Example 1Example 1 Example 2Example 2
ExercisesExercises
Arrange the terms of each polynomial so that the powers of x are in ascending order.
1. 5x x2 6 2. 6x 9 � 4x2 3. 4xy 2y 6x2
4. 6y2x � 6x2y 2 5. x4 x3 x2 6. 2x3 � x 3x7
7. �5cx 10c2x3 15cx2 8. �4nx � 5n3x3 5 9. 4xy 2y 5x2
Arrange the terms of each polynomial so that the powers of x are in descending order.
10. 2x x2 � 5 11. 20x � 10x2 5x3 12. x2 4yx� 10x5
13. 9bx 3bx2 � 6x3 14. x3 x5 � x2 15. ax2 8a2x5 � 4
16. 3x3y � 4xy2 � x4y2 y5 17. x4 4x3 � 7x5 1
18. �3x6 � x5 2x8 19. �15cx2 8c2x5 cx
20. 24x2y � 12x3y2 6x4 21. �15x3 10x4y2 7xy2
Skills PracticePolynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-48-4
© Glencoe/McGraw-Hill 475 Glencoe Algebra 1
Less
on
8-4
State whether each expression is a polynomial. If the expression is a polynomial,identify it as a monomial, a binomial, or a trinomial.
1. 5mn n2 2. 4by 2b � by 3. �32
4. 5. 5x2 � 3x�4 6. 2c2 8c 9 � 3
GEOMETRY Write a polynomial to represent the area of each shaded region.
7. 8.
Find the degree of each polynomial.
9. 12 10. 3r4 11. b 6
12. 4a3 � 2a 13. 5abc � 2b2 1 14. 8x5y4 � 2x8
Arrange the terms of each polynomial so that the powers of x are in ascendingorder.
15. 3x 1 2x2 16. 5x � 6 3x2
17. 9x2 2 x3 x 18. �3 3x3 � x2 4x
19. 7r5x 21r4 � r2x2 � 15x3 20. 3a2x4 14a2 � 10x3 ax2
Arrange the terms of each polynomial so that the powers of x are in descendingorder.
21. x2 3x3 27 � x 22. 25 � x3 x
23. x � 3x2 4 5x3 24. x2 64 � x 7x3
25. 2cx 32 � c3x2 6x3 26. 13 � x3y3 x2y2 x
r
a
x
by
3x�7
© Glencoe/McGraw-Hill 476 Glencoe Algebra 1
State whether each expression is a polynomial. If the expression is a polynomial,identify it as a monomial, a binomial, or a trinomial.
1. 7a2b 3b2 � a2b 2. y3 y2 � 9 3. 6g2h3k
GEOMETRY Write a polynomial to represent the area of each shaded region.
4. 5.
Find the degree of each polynomial.
6. x 3x4 � 21x2 x3 7. 3g2h3 g3h
8. �2x2y 3xy3 x2 9. 5n3m � 2m3 n2m4 n2
10. a3b2c 2a5c b3c2 11. 10s2t2 4st2 � 5s3t2
Arrange the terms of each polynomial so that the powers of x are in ascendingorder.
12. 8x2 � 15 5x5 13. 10bx � 7b2 x4 4b2x3
14. �3x3y 8y2 xy4 15. 7ax � 12 3ax3 a2x2
Arrange the terms of each polynomial so that the powers of x are in descendingorder.
16. 13x2 � 5 6x3 � x 17. 4x 2x5 � 6x3 2
18. g2x � 3gx3 7g3 4x2 19. �11x2y3 6y � 2xy 2x4
20. 7a2x2 17 � a3x3 2ax 21. 12rx3 9r6 r2x 8x6
22. MONEY Write a polynomial to represent the value of t ten-dollar bills, f fifty-dollarbills, and h one-hundred-dollar bills.
23. GRAVITY The height above the ground of a ball thrown up with a velocity of 96 feet persecond from a height of 6 feet is 6 96t � 16t2 feet, where t is the time in seconds.According to this model, how high is the ball after 7 seconds? Explain.
da
b
b
1�5
Practice Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-48-4
Reading to Learn MathematicsPolynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-48-4
© Glencoe/McGraw-Hill 477 Glencoe Algebra 1
Less
on
8-4
Pre-Activity How are polynomials useful in modeling data?
Read the introduction to Lesson 8-4 at the top of page 432 in your textbook.
• How many terms does t4 � 9t3 � 26t � 18t � 76 have?
• What could you call a polynomial with just one term?
Reading the Lesson
1. What is the meaning of the prefixes mono-, bi-, and tri-?
2. Write examples of words that begin with the prefixes mono-, bi-, and tri-.
3. Complete the table.
monomial binomial trinomialpolynomial with more
than three terms
Example 3r 2t 2x2 � 3x 5x2 � 3x � 2 7s2 � s4 � 2s3 � s � 5
Number of Terms
4. What is the degree of the monomial 3xy2z?
5. What is the degree of the polynomial 4x4 � 2x3y3 � y2 � 14? Explain how you foundyour answer.
Helping You Remember
6. Use a dictionary to find the meaning of the terms ascending and descending. Write theirmeanings and then describe a situation in your everyday life that relates to them.
© Glencoe/McGraw-Hill 478 Glencoe Algebra 1
Polynomial FunctionsSuppose a linear equation such as 23x � y � 4 is solved for y. Then an equivalent equation,y � 3x � 4, is found. Expressed in this way, y is a function of x, or f(x) � 3x � 4. Notice that the right side of the equation is a binomial of degree 1.
Higher-degree polynomials in x may also form functions. An example is f(x) � x3 � 1, which is a polynomial function of degree 3. You can graph this function using a table of ordered pairs, as shown at the right.
For each of the following polynomial functions, make a tableof values for x and y � f(x). Then draw the graph on the grid.
1. f(x) � 1 � x2 2. f(x) � x2 � 5
3. f(x) � x2 � 4x � 1 4. f(x) � x3
x
y
Ox
y
O
x
y
Ox
y
O
x
y
O
x y
�1�12
� �2�38
�
�1 0
0 1
1 2
1�12
� 4 �38
�
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
8-48-4
Study Guide and InterventionAdding and Subtracting Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
6-58-5
© Glencoe/McGraw-Hill 479 Glencoe Algebra 1
Less
on
8-5
Add Polynomials To add polynomials, you can group like terms horizontally or writethem in column form, aligning like terms vertically. Like terms are monomial terms thatare either identical or differ only in their coefficients, such as 3p and �5p or 2x2y and 8x2y.
Find (2x2 � x � 8) �(3x � 4x2 � 2).
Horizontal MethodGroup like terms.
(2x2 � x � 8) � (3x � 4x2 � 2)� [(2x2 � (�4x2)] � (x � 3x ) � [(�8) � 2)]� �2x2 � 4x � 6.
The sum is �2x2 � 4x � 6.
Find (3x2 � 5xy) �(xy � 2x2).
Vertical MethodAlign like terms in columns and add.
3x2 � 5xy(�) 2x2 � xy Put the terms in descending order.
5x2 � 6xy
The sum is 5x2 � 6xy.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each sum.
1. (4a � 5) � (3a � 6) 2. (6x � 9) � (4x2 � 7)
3. (6xy � 2y � 6x) � (4xy � x) 4. (x2 � y2) � (�x2 � y2)
5. (3p2 � 2p � 3) � (p2 � 7p � 7) 6. (2x2 � 5xy � 4y2) � (�xy � 6x2 � 2y2)
7. (5p � 2q) � (2p2 � 8q � 1) 8. (4x2 � x � 4) � (5x � 2x2 � 2)
9. (6x2 � 3x) � (x2 � 4x � 3) 10. (x2 � 2xy � y2) � (x2 � xy � 2y2)
11. (2a � 4b � c) � (�2a � b � 4c) 12. (6xy2 � 4xy) � (2xy � 10xy2 � y2)
13. (2p � 5q) � (3p � 6q) � (p � q) 14. (2x2 � 6) � (5x2 � 2) � (�x2 � 7)
15. (3z2 � 5z) � (z2 � 2z) � (z � 4) 16. (8x2 � 4x � 3y2 � y) � (6x2 � x � 4y)
© Glencoe/McGraw-Hill 480 Glencoe Algebra 1
Subtract Polynomials You can subtract a polynomial by adding its additive inverse.To find the additive inverse of a polynomial, replace each term with its additive inverse or opposite.
Find (3x2 � 2x � 6) � (2x � x2 � 3).
Study Guide and Intervention (continued)
Adding and Subtracting Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-58-5
ExampleExample
Horizontal Method
Use additive inverses to rewrite as addition.Then group like terms.
(3x2 � 2x � 6) � (2x � x2 � 3)� (3x2 � 2x � 6) � [(�2x)� (�x2) � (�3)]� [3x2 � (�x2)] � [2x � (�2x)] � [�6 � (�3)]� 2x2 � (�9)� 2x2 � 9
The difference is 2x2 � 9.
Vertical Method
Align like terms in columns andsubtract by adding the additive inverse.
3x2 � 2x � 6(�) x2 � 2x � 3
3x2 � 2x � 6(�) �x2 � 2x � 3
2x2 � 9The difference is 2x2 � 9.
ExercisesExercises
Find each difference.
1. (3a � 5) � (5a � 1) 2. (9x � 2) � (�3x2 � 5)
3. (9xy � y � 2x) � (6xy � 2x) 4. (x2 � y2) � (�x2 � y2)
5. (6p2 � 4p � 5) � (2p2 � 5p � 1) 6. (6x2 � 5xy � 2y2) � (�xy � 2x2 � 4y2)
7. (8p � 5q) � (�6p2 � 6q � 3) 8. (8x2 � 4x � 3) � (�2x � x2 � 5)
9. (3x2 � 2x) � (3x2 � 5x � 1) 10. (4x2 � 6xy � 2y2) � (�x2 � 2xy � 5y2)
11. (2h � 6j � 2k) � (�7h � 5j � 4k) 12. (9xy2 � 5xy) � (�2xy � 8xy2)
13. (2a � 8b) � (�3a � 5b) 14. (2x2 � 8) � (�2x2 � 6)
15. (6z2 � 4z � 2) � (4z2 � z) 16. (6x2 � 5x � 1) � (�7x2 � 2x � 4)
Skills PracticeAdding and Subtracting Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-58-5
© Glencoe/McGraw-Hill 481 Glencoe Algebra 1
Less
on
8-5
Find each sum or difference.
1. (2x � 3y) � (4x � 9y) 2. (6s � 5t) � (4t � 8s)
3. (5a � 9b) � (2a � 4b) 4. (11m � 7n) � (2m � 6n)
5. (m2 � m) � (2m � m2) 6. (x2 � 3x) � (2x2 � 5x)
7. (d2 � d � 5) � (2d � 5) 8. (2e2 � 5e) � (7e � 3e2)
9. (5f � g � 2) � (�2f � 3) 10. (6k2 � 2k � 9) � (4k2 � 5k)
11. (x3 � x � 1) � (3x � 1) 12. (b2 � ab � 2) � (2b2 � 2ab)
13. (7z2 � 4 � z) � (�5 � 3z2) 14. (5 � 4n � 2m) � (�6m � 8)
15. (4t2 � 2) � (�4 � 2t) 16. (3g3 � 7g) � (4g � 8g3)
17. (2a2 � 8a � 4) � (a2 � 3) 18. (3x2 � 7x � 5) � (�x2 � 4x)
19. (7z2 � z � 1) � (�4z � 3z2 � 3) 20. (2c2 � 7c � 4) � (c2 � 1 � 9c)
21. (n2 � 3n � 2) � (2n2 � 6n � 2) 22. (a2 � ab � 3b2) � (b2 � 4a2 � ab)
23. (�2 � 5� � 6) � (2�2 � 5 � �) 24. (2m2 � 5m � 1) � (4m2 � 3m � 3)
25. (x2 � 6x � 2) � (�5x2 � 7x � 4) 26. (5b2 � 9b � 5) � (b2 � 6 � 2b)
27. (2x2 � 6x � 2) � (x2 � 4x) � (3x2 � x � 5)
© Glencoe/McGraw-Hill 482 Glencoe Algebra 1
Find each sum or difference.
1. (4y � 5) � (�7y � 1) 2. (�x2 � 3x) � (5x � 2x2)
3. (4k2 � 8k � 2) � (2k � 3) 4. (2m2 � 6m) � (m2 � 5m � 7)
5. (2w2 � 3w � 1) � (4w � 7) 6. (g3 � 2g2) � (6g � 4g2 � 2g3)
7. (5a2 � 6a � 2) � (7a2 � 7a � 5) 8. (�4p2 � p � 9) � (p2 � 3p � 1)
9. (x3 � 3x � 1) � (x3 � 7 � 12x) 10. (6c2 � c � 1) � (�4 � 2c2 � 8c)
11. (�b3 � 8bc2 � 5) � (7bc2 � 2 � b3) 12. (5n2 � 3n � 2) � (�n � 2n2 � 4)
13. (4y2 � 2y � 8) � (7y2 � 4 � y) 14. (w2 � 4w � 1) � (�5 � 5w2 � 3w)
15. (4u2 � 2u � 3) � (3u2 � u � 4) 16. (5b2 � 8 � 2b) � (b � 9b2 � 5)
17. (4d2 � 2d � 2) � (5d2 � 2 � d) 18. (8x2 � x � 6) � (�x2 � 2x � 3)
19. (3h2 � 7h � 1) � (4h � 8h2 � 1) 20. (4m2 � 3m � 10) � (m2 � m � 2)
21. (x2 � y2 � 6) � (5x2 � y2 � 5) 22. (7t2 � 2 � t) � (t2 � 7 � 2t)
23. (k3 � 2k2 � 4k � 6) � (�4k � k2 � 3) 24. (9j2 � j � jk) � (�3j2 � jk � 4j)
25. (2x � 6y � 3z) � (4x � 6z � 8y) � (x � 3y � z)
26. (6f 2 � 7f � 3) � (5f 2 � 1 � 2f ) � (2f 2 � 3 � f )
27. BUSINESS The polynomial s3 � 70s2 � 1500s � 10,800 models the profit a companymakes on selling an item at a price s. A second item sold at the same price brings in aprofit of s3 � 30s2 � 450s � 5000. Write a polynomial that expresses the total profitfrom the sale of both items.
28. GEOMETRY The measures of two sides of a triangle are given.If P is the perimeter, and P � 10x � 5y, find the measure of the third side.
3x � 4y
5x � y
Practice Adding and Subtracting Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-58-5
Reading to Learn MathematicsAdding and Subtracting Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-58-5
© Glencoe/McGraw-Hill 483 Glencoe Algebra 1
Less
on
8-5
Pre-Activity How can adding polynomials help you model sales?
Read the introduction to Lesson 8-5 at the top of page 439 in your textbook.
What operation would you use to find how much more the traditional toysales R were than the video games sales V ?
Reading the Lesson
1. Use the example (�3x3 � 4x2 � 5x � 1) � (�5x3 � 2x2 � 2x � 7).
a. Show what is meant by grouping like terms horizontally.
b. Show what is meant by aligning like terms vertically.
c. Choose one method, then add the polynomials.
2. How is subtracting a polynomial like subtracting a rational number?
3. An algebra student got the following exercise wrong on his homework. What was his error?
(3x5 � 3x4 � 2x3 � 4x2 � 5) � (2x5 � x3 � 2x2 � 4)� [3x5 � (�2x5)] � (�3x4) � [2x3 � (�x3)] � [�4x2 � (�2x2)] � (5 � 4)� x5 � 3x4 � x3 � 6x2 � 9
Helping You Remember
4. How is adding and subtracting polynomials vertically like adding and subtractingdecimals vertically?
© Glencoe/McGraw-Hill 484 Glencoe Algebra 1
Circular Areas and Volumes
Area of Circle Volume of Cylinder Volume of Cone
A � �r2 V � �r2h V � �r2h
Write an algebraic expression for each shaded area. (Recall that the diameter of a circle is twice its radius.)
1. 2. 3.
Write an algebraic expression for the total volume of each figure.
4. 5.
Each figure has a cylindrical hole with a radius of 2 inches and a height of 5 inches. Find each volume.
6. 7.
3x
4x
5x
7x
3x—2
x � a
x
x � b
x
2x5x
3x2x2x x
y x x yx
x
r
h
r
h
r
1�3
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
8-58-5
Study Guide and InterventionMultiplying a Polynomial by a Monomial
NAME ______________________________________________ DATE ____________ PERIOD _____
8-68-6
© Glencoe/McGraw-Hill 485 Glencoe Algebra 1
Less
on
8-6
Product of Monomial and Polynomial The Distributive Property can be used tomultiply a polynomial by a monomial. You can multiply horizontally or vertically. Sometimesmultiplying results in like terms. The products can be simplified by combining like terms.
Find �3x2(4x2 � 6x � 8).
Horizontal Method�3x2(4x2 � 6x � 8)
� �3x2(4x2) � (�3x2)(6x) � (�3x2)(8)� �12x4 � (�18x3) � (�24x2)� �12x4 � 18x3 � 24x2
Vertical Method4x2 � 6x � 8
(�) �3x2
�12x4 � 18x3 � 24x2
The product is �12x4 � 18x3 � 24x2.
Simplify �2(4x2 � 5x) �x(x2 � 6x).
�2(4x2 � 5x) � x( x2 � 6x)� �2(4x2) � (�2)(5x) � (�x)(x2) � (�x)(6x)� �8x2 � (�10x) � (�x3) � (�6x2)� (�x3) � [�8x2 � (�6x2)] � (�10x)� �x3 � 14x2 � 10x
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each product.
1. x(5x � x2) 2. x(4x2 � 3x � 2) 3. �2xy(2y � 4x2)
4. �2g( g2 � 2g � 2) 5. 3x(x4 � x3� x2) 6. �4x(2x3 � 2x � 3)
7. �4cx(10 � 3x) 8. 3y(�4x � 6x3� 2y) 9. 2x2y2(3xy � 2y � 5x)
Simplify.
10. x(3x � 4) � 5x 11. �x(2x2 � 4x) � 6x2
12. 6a(2a � b) � 2a(�4a � 5b) 13. 4r(2r2 � 3r � 5) � 6r(4r2 � 2r � 8)
14. 4n(3n2 � n � 4) � n(3 � n) 15. 2b(b2 � 4b � 8) � 3b(3b2 � 9b � 18)
16. �2z(4z2 � 3z � 1) � z(3z2 � 2z � 1) 17. 2(4x2 � 2x) � 3(�6x2 � 4) � 2x(x � 1)
© Glencoe/McGraw-Hill 486 Glencoe Algebra 1
Solve Equations with Polynomial Expressions Many equations containpolynomials that must be added, subtracted, or multiplied before the equation can be solved.
Solve 4(n � 2) � 5n � 6(3 � n) � 19.
4(n � 2) � 5n � 6(3 � n) � 19 Original equation
4n � 8 � 5n � 18 � 6n � 19 Distributive Property
9n � 8 � 37 � 6n Combine like terms.
15n � 8 � 37 Add 6n to both sides.
15n � 45 Add 8 to both sides.
n � 3 Divide each side by 15.
The solution is 3.
Solve each equation.
1. 2(a � 3) � 3(�2a � 6) 2. 3(x � 5) � 6 � 18
3. 3x(x � 5) � 3x2 � �30 4. 6(x2 � 2x) � 2(3x2 � 12)
5. 4(2p � 1) � 12p � 2(8p � 12) 6. 2(6x � 4) � 2 � 4(x � 4)
7. �2(4y � 3) � 8y � 6 � 4(y � 2) 8. c(c � 2) � c(c � 6) � 10c � 12
9. 3(x2 � 2x) � 3x2 � 5x � 11 10. 2(4x � 3) � 2 � �4(x � 1)
11. 3(2h � 6) � (2h � 1) � 9 12. 3(y � 5) � (4y � 8) � �2y � 10
13. 3(2a � 6) � (�3a � 1) � 4a � 2 14. 5(2x2 � 1) � (10x2 � 6) � �(x � 2)
15. 3(x � 2) � 2(x � 1) � �5(x � 3) 16. 4(3p2 � 2p) � 12p2 � 2(8p � 6)
Study Guide and Intervention (continued)
Multiplying a Polynomial by a Monomial
NAME ______________________________________________ DATE ____________ PERIOD _____
8-68-6
ExampleExample
ExercisesExercises
Skills PracticeMultiplying a Polynomial by a Monomial
NAME ______________________________________________ DATE ____________ PERIOD _____
8-68-6
© Glencoe/McGraw-Hill 487 Glencoe Algebra 1
Less
on
8-6
Find each product.
1. a(4a � 3) 2. �c(11c � 4)
3. x(2x � 5) 4. 2y(y � 4)
5. �3n(n2 � 2n) 6. 4h(3h � 5)
7. 3x(5x2 � x � 4) 8. 7c(5 � 2c2 � c3)
9. �4b(1 � 9b � 2b2) 10. 6y(�5 � y � 4y2)
11. 2m2(2m2 � 3m � 5) 12. �3n2(�2n2 � 3n � 4)
Simplify.
13. w(3w � 2) � 5w 14. f(5f � 3) � 2f
15. �p(2p � 8) � 5p 16. y2(�4y � 5) � 6y2
17. 2x(3x2 � 4) � 3x3 18. 4a(5a2 � 4) � 9a
19. 4b(�5b � 3) � 2(b2 � 7b � 4) 20. 3m(3m � 6) � 3(m2 � 4m � 1)
Solve each equation.
21. 3(a � 2) � 5 � 2a � 4 22. 2(4x � 2) � 8 � 4(x � 3)
23. 5( y � 1) � 2 � 4( y � 2) � 6 24. 4(b � 6) � 2(b � 5) � 2
25. 6(m � 2) � 14 � 3(m � 2) � 10 26. 3(c � 5) � 2 � 2(c � 6) � 2
© Glencoe/McGraw-Hill 488 Glencoe Algebra 1
Find each product.
1. 2h(�7h2 � 4h) 2. 6pq(3p2 � 4q) 3. �2u2n(4u � 2n)
4. 5jk(3jk � 2k) 5. �3rs(�2s2 � 3r) 6. 4mg2(2mg � 4g)
7. � m(8m2 � m � 7) 8. � n2(�9n2 � 3n � 6)
Simplify.
9. �2�(3� � 4) � 7� 10. 5w(�7w � 3) � 2w(�2w2 � 19w � 2)
11. 6t(2t � 3) � 5(2t2 � 9t � 3) 12. �2(3m3 � 5m � 6) � 3m(2m2 � 3m � 1)
13. �3g(7g � 2) � 3(g2 � 2g � 1) � 3g(�5g � 3)
14. 4z2(z � 7) � 5z(z2 � 2z � 2) � 3z(4z � 2)
Solve each equation.
15. 5(2s � 1) � 3 � 3(3s � 2) 16. 3(3u � 2) � 5 � 2(2u � 2)
17. 4(8n � 3) � 5 � 2(6n � 8) � 1 18. 8(3b � 1) � 4(b � 3) � 9
19. h(h � 3) � 2h � h(h � 2) � 12 20. w(w � 6) � 4w � �7 � w(w � 9)
21. t(t � 4) � 1 � t(t � 2) � 2 22. u(u � 5) � 8u � u(u � 2) � 4
23. NUMBER THEORY Let x be an integer. What is the product of twice the integer addedto three times the next consecutive integer?
INVESTMENTS For Exercises 24–26, use the following information.Kent invested $5,000 in a retirement plan. He allocated x dollars of the money to a bondaccount that earns 4% interest per year and the rest to a traditional account that earns 5%interest per year.
24. Write an expression that represents the amount of money invested in the traditionalaccount.
25. Write a polynomial model in simplest form for the total amount of money T Kent hasinvested after one year. (Hint: Each account has A � IA dollars, where A is the originalamount in the account and I is its interest rate.)
26. If Kent put $500 in the bond account, how much money does he have in his retirementplan after one year?
2�3
1�4
Practice Multiplying a Polynomial by a Monomial
NAME ______________________________________________ DATE ____________ PERIOD _____
8-68-6
Reading to Learn MathematicsMultiplying a Polynomial by a Monomial
NAME ______________________________________________ DATE ____________ PERIOD _____
8-68-6
© Glencoe/McGraw-Hill 489 Glencoe Algebra 1
Less
on
8-6
Pre-Activity How is finding the product of a monomial and a polynomial relatedto finding the area of a rectangle?
Read the introduction to Lesson 8-6 at the top of page 444 in your textbook.
You may recall that the formula for the area of a rectangle is A � �w. In
this rectangle, � � and w � . How would you
substitute these values in the area formula?
Reading the Lesson
1. Refer to Lesson 8-6.
a. How is the Distributive Property used to multiply a polynomial by a monomial?
b. Use the Distributive Property to complete the following.
2y2(3y2 � 2y � 7) � 2y2( ) � 2y2( ) � 2y2( )
� � �
�3x3(x3 � 2x2 � 3) � � �
� � �
2. What is the difference between simplifying an expression and solving an equation?
Helping You Remember
3. Use the equation 2x(x � 5) � 3x(x � 3) � 5x(x � 7) � 9 to show how you would explainthe process of solving equations with polynomial expressions to another algebra student.
© Glencoe/McGraw-Hill 490 Glencoe Algebra 1
Figurate NumbersThe numbers below are called pentagonal numbers. They are the numbers of dots or disksthat can be arranged as pentagons.
1. Find the product n(3n � 1).
2. Evaluate the product in Exercise 1 for values of n from 1 through 4.
3. What do you notice?
4. Find the next six pentagonal numbers.
5. Find the product n(n � 1).
6. Evaluate the product in Exercise 5 for values of n from 1 through 5. On another sheet ofpaper, make drawings to show why these numbers are called the triangular numbers.
7. Find the product n(2n � 1).
8. Evaluate the product in Exercise 7 for values of n from 1 through 5. Draw thesehexagonal numbers.
9. Find the first 5 square numbers. Also, write the general expression for any squarenumber.
The numbers you have explored above are called the plane figurate numbers because theycan be arranged to make geometric figures. You can also create solid figurate numbers.
10. If you pile 10 oranges into a pyramid with a triangle as a base, you get one of thetetrahedral numbers. How many layers are there in the pyramid? How many orangesare there in the bottom layers?
11. Evaluate the expression n3 � n2 � n for values of n from 1 through 5 to find the
first five tetrahedral numbers.
1�3
1�2
1�6
1�2
1�2
●●
221251
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
8-68-6
Study Guide and InterventionMultiplying Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-78-7
© Glencoe/McGraw-Hill 491 Glencoe Algebra 1
Less
on
8-7
Multiply Binomials To multiply two binomials, you can apply the Distributive Propertytwice. A useful way to keep track of terms in the product is to use the FOIL method asillustrated in Example 2.
Find (x � 3)(x � 4).
Horizontal Method(x � 3)(x � 4)
� x(x � 4) � 3(x � 4)� (x)(x) � x(�4) � 3(x)� 3(�4)� x2 � 4x � 3x � 12� x2 � x � 12
Vertical Method
x � 3(�) x � 4
�4x � 12x2 � 3xx2 � x � 12
The product is x2 � x � 12.
Find (x � 2)(x � 5) usingthe FOIL method.
(x � 2)(x � 5)First Outer Inner Last
� (x)(x) � (x)(5) � (�2)(x) � (�2)(5)� x2 � 5x � (�2x) � 10� x2 � 3x � 10
The product is x2 � 3x � 10.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each product.
1. (x � 2)(x � 3) 2. (x � 4)(x � 1) 3. (x � 6)(x � 2)
4. (p � 4)(p � 2) 5. (y � 5)(y � 2) 6. (2x � 1)(x � 5)
7. (3n � 4)(3n � 4) 8. (8m � 2)(8m � 2) 9. (k � 4)(5k � 1)
10. (3x � 1)(4x � 3) 11. (x � 8)(�3x � 1) 12. (5t � 4)(2t � 6)
13. (5m � 3n)(4m � 2n) 14. (a � 3b)(2a � 5b) 15. (8x � 5)(8x � 5)
16. (2n � 4)(2n � 5) 17. (4m � 3)(5m � 5) 18. (7g � 4)(7g � 4)
© Glencoe/McGraw-Hill 492 Glencoe Algebra 1
Multiply Polynomials The Distributive Property can be used to multiply any two polynomials.
Find (3x � 2)(2x2 � 4x � 5).
(3x � 2)(2x2 � 4x � 5)� 3x(2x2 � 4x � 5) � 2(2x2 � 4x � 5) Distributive Property
� 6x3 � 12x2 � 15x � 4x2 � 8x � 10 Distributive Property
� 6x3 � 8x2 � 7x � 10 Combine like terms.
The product is 6x3 � 8x2 � 7x � 10.
Find each product.
1. (x � 2)(x2 � 2x � 1) 2. (x � 3)(2x2 � x � 3)
3. (2x � 1)(x2 � x � 2) 4. (p � 3)(p2 � 4p � 2)
5. (3k � 2)(k2 � k � 4) 6. (2t � 1)(10t2 � 2t � 4)
7. (3n � 4)(n2 � 5n � 4) 8. (8x � 2)(3x2 � 2x � 1)
9. (2a � 4)(2a2 � 8a � 3) 10. (3x � 4)(2x2 � 3x � 3)
11. (n2 � 2n � 1)(n2 � n � 2) 12. (t2 � 4t � 1)(2t2 � t � 3)
13. (y2 � 5y � 3)(2y2 � 7y � 4) 14. (3b2 � 2b � 1)(2b2 � 3b � 4)
Study Guide and Intervention (continued)
Multiplying Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-78-7
ExampleExample
ExercisesExercises
Skills PracticeMultiplying Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-78-7
© Glencoe/McGraw-Hill 493 Glencoe Algebra 1
Less
on
8-7
Find each product.
1. (m � 4)(m � 1) 2. (x � 2)(x � 2)
3. (b � 3)(b � 4) 4. (t � 4)(t � 3)
5. (r � 1)(r � 2) 6. (z � 5)(z � 1)
7. (3c � 1)(c � 2) 8. (2x � 6)(x � 3)
9. (d � 1)(5d � 4) 10. (2� � 5)(� � 4)
11. (3n � 7)(n � 3) 12. (q � 5)(5q � 1)
13. (3b � 3)(3b � 2) 14. (2m � 2)(3m � 3)
15. (4c � 1)(2c � 1) 16. (5a � 2)(2a � 3)
17. (4h � 2)(4h � 1) 18. (x � y)(2x � y)
19. (e � 4)(e2 � 3e � 6) 20. (t � 1)(t2 � 2t � 4)
21. (k � 4)(k2 � 3k � 6) 22. (m � 3)(m2 � 3m � 5)
GEOMETRY Write an expression to represent the area of each figure.
23. 24.
2x � 4
2x � 5
4x � 1
© Glencoe/McGraw-Hill 494 Glencoe Algebra 1
Find each product.
1. (q � 6)(q � 5) 2. (x � 7)(x � 4) 3. (s � 5)(s � 6)
4. (n � 4)(n � 6) 5. (a � 5)(a � 8) 6. (w � 6)(w � 9)
7. (4c � 6)(c � 4) 8. (2x � 9)(2x � 4) 9. (4d � 5)(2d � 3)
10. (4b � 3)(3b � 4) 11. (4m � 2)(4m � 3) 12. (5c � 5)(7c � 9)
13. (6a � 3)(7a � 4) 14. (6h � 3)(4h � 2) 15. (2x � 2)(5x � 4)
16. (3a � b)(2a � b) 17. (4g � 3h)(2g � 3h) 18. (4x � y)(4x � y)
19. (m � 5)(m2 � 4m � 8) 20. (t � 3)(t2 � 4t � 7)
21. (2h � 3)(2h2 � 3h � 4) 22. (3d � 3)(2d2 � 5d � 2)
23. (3q � 2)(9q2 � 12q � 4) 24. (3r � 2)(9r2 � 6r � 4)
25. (3c2 � 2c � 1)(2c2 � c � 9) 26. (2�2 � � � 3)(4�2 � 2� � 2)
27. (2x2 � 2x � 3)(2x2 � 4x � 3) 28. (3y2 � 2y � 2)(3y2 � 4y � 5)
GEOMETRY Write an expression to represent the area of each figure.
29. 30.
31. NUMBER THEORY Let x be an even integer. What is the product of the next twoconsecutive even integers?
32. GEOMETRY The volume of a rectangular pyramid is one third the product of the areaof its base and its height. Find an expression for the volume of a rectangular pyramidwhose base has an area of 3x2 � 12x � 9 square feet and whose height is x � 3 feet.
3x � 2
5x � 4
x � 1
4x � 2
2x � 2
Practice Multiplying Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-78-7
Reading to Learn MathematicsMultiplying Polynomials
NAME ______________________________________________ DATE ____________ PERIOD _____
8-78-7
© Glencoe/McGraw-Hill 495 Glencoe Algebra 1
Less
on
8-7
Pre-Activity How is multiplying binomials similar to multiplying two-digitnumbers?
Read the introduction to Lesson 8-7 at the top of page 452 in your textbook.
In your own words, explain how the distributive property is used twice tomultiply two-digit numbers.
Reading the Lesson
1. How is multiplying binomials similar to multiplying two-digit numbers?
2. Complete the table using the FOIL method.
Product of�
Product of�
Product of�
Product of First Terms Outer Terms Inner Terms Last Terms
(x � 5)(x � 3) � � � �
� � � �
� � �
(3y � 6)(y � 2) � � � �
� � � �
� �
Helping You Remember
3. Think of a method for remembering all the product combinations used in the FOILmethod for multiplying two binomials. Describe your method using words or a diagram.
© Glencoe/McGraw-Hill 496 Glencoe Algebra 1
Pascal’s TriangleThis arrangement of numbers is called Pascal’s Triangle.It was first published in 1665, but was known hundreds of years earlier.
1. Each number in the triangle is found by adding two numbers.What two numbers were added to get the 6 in the 5th row?
2. Describe how to create the 6th row of Pascal’s Triangle.
3. Write the numbers for rows 6 through 10 of the triangle.
Row 6:
Row 7:
Row 8:
Row 9:
Row 10:
Multiply to find the expanded form of each product.
4. (a � b)2
5. (a � b)3
6. (a � b)4
Now compare the coefficients of the three products in Exercises 4–6 with Pascal’s Triangle.
7. Describe the relationship between the expanded form of (a � b)n and Pascal’s Triangle.
8. Use Pascal’s Triangle to write the expanded form of (a � b)6.
11 1
1 2 11 3 3 1
1 4 6 4 1
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
8-78-7
Study Guide and InterventionSpecial Products
NAME ______________________________________________ DATE ____________ PERIOD _____
8-88-8
© Glencoe/McGraw-Hill 497 Glencoe Algebra 1
Less
on
8-8
Squares of Sums and Differences Some pairs of binomials have products thatfollow specific patterns. One such pattern is called the square of a sum. Another is called thesquare of a difference.
Square of a sum (a � b)2 � (a � b)(a � b) � a2 � 2ab � b2
Square of a difference (a � b)2 � (a � b)(a � b) � a2 � 2ab � b2
Find (3a � 4)(3a � 4).
Use the square of a sum pattern, with a �3a and b � 4.
(3a � 4)(3a � 4) � (3a)2 � 2(3a)(4) � (4)2
� 9a2 � 24a � 16
The product is 9a2 � 24a � 16.
Find (2z � 9)(2z � 9).
Use the square of a difference pattern witha � 2z and b � 9.
(2z � 9)(2z � 9) � (2z)2 � 2(2z)(9) � (9)(9)� 4z2 � 36z � 81
The product is 4z2 � 36z � 81.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each product.
1. (x � 6)2 2. (3p � 4)2 3. (4x � 5)2
4. (2x � 1)2 5. (2h � 3)2 6. (m � 5)2
7. (c � 3)2 8. (3 � p)2 9. (x � 5y)2
10. (8y � 4)2 11. (8 � x)2 12. (3a � 2b)2
13. (2x � 8)2 14. (x2 � 1)2 15. (m2 � 2)2
16. (x3 � 1)2 17. (2h2 � k2)2 18. � x � 3�2
19. (x � 4y2)2 20. (2p � 4q)2 21. � x � 2�22�3
1�4
© Glencoe/McGraw-Hill 498 Glencoe Algebra 1
Product of a Sum and a Difference There is also a pattern for the product of asum and a difference of the same two terms, (a � b)(a � b). The product is called thedifference of squares.
Product of a Sum and a Difference (a � b)(a � b) � a2 � b2
Find (5x � 3y)(5x � 3y).
(a � b)(a � b) � a2 � b2 Product of a Sum and a Difference
(5x � 3y)(5x � 3y) � (5x)2 � (3y)2 a � 5x and b � 3y
� 25x2 � 9y2 Simplify.
The product is 25x2 � 9y2.
Find each product.
1. (x � 4)(x � 4) 2. (p � 2)(p � 2) 3. (4x � 5)(4x � 5)
4. (2x � 1)(2x � 1) 5. (h � 7)(h � 7) 6. (m � 5)(m � 5)
7. (2c � 3)(2c � 3) 8. (3 � 5q)(3 � 5q) 9. (x � y)(x � y)
10. ( y � 4x)( y � 4x) 11. (8 � 4x)(8 � 4x) 12. (3a � 2b)(3a � 2b)
13. (3y � 8)(3y � 8) 14. (x2 � 1)(x2 � 1) 15. (m2 � 5)(m2 � 5)
16. (x3 � 2)(x3 � 2) 17. (h2 � k2)(h2 � k2) 18. � x � 2�� x � 2�
19. (3x � 2y2)(3x � 2y2) 20. (2p � 5s)(2p � 5s) 21. � x � 2y�� x � 2y�4�3
4�3
1�4
1�4
Study Guide and Intervention (continued)
Special Products
NAME ______________________________________________ DATE ____________ PERIOD _____
8-88-8
ExampleExample
ExercisesExercises
Skills PracticeSpecial Products
NAME ______________________________________________ DATE ____________ PERIOD _____
8-88-8
© Glencoe/McGraw-Hill 499 Glencoe Algebra 1
Less
on
8-8
Find each product.
1. (n � 3)2 2. (x � 4)(x � 4)
3. ( y � 7)2 4. (t � 3)(t � 3)
5. (b � 1)(b � 1) 6. (a � 5)(a � 5)
7. (p � 4)2 8. (z � 3)(z � 3)
9. (� � 2)(� � 2) 10. (r � 1)(r � 1)
11. (3g � 2)(3g � 2) 12. (2m � 3)(2m � 3)
13. (6 � u)2 14. (r � s)2
15. (3q � 1)(3q � 1) 16. (c � e)2
17. (2k � 2)2 18. (w � 3h)2
19. (3p � 4)(3p � 4) 20. (t � 2u)2
21. (x � 4y)2 22. (3b � 7)(3b � 7)
23. (3y � 3g)(3y � 3g) 24. (s2 � r2)2
25. (2k � m2)2 26. (3u2 � n)2
27. GEOMETRY The length of a rectangle is the sum of two whole numbers. The width ofthe rectangle is the difference of the same two whole numbers. Using these facts, write averbal expression for the area of the rectangle.
© Glencoe/McGraw-Hill 500 Glencoe Algebra 1
Find each product.
1. (n � 9)2 2. (q � 8)2 3. (� � 10)2
4. (r � 11)2 5. ( p � 7)2 6. (b � 6)(b � 6)
7. (z � 13)(z � 13) 8. (4e � 2)2 9. (5w � 4)2
10. (6h � 1)2 11. (3s � 4)2 12. (7v � 2)2
13. (7k � 3)(7k � 3) 14. (4d � 7)(4d � 7) 15. (3g � 9h)(3g � 9h)
16. (4q � 5t)(4q � 5t) 17. (a � 6u)2 18. (5r � s)2
19. (6c � m)2 20. (k � 6y)2 21. (u � 7p)2
22. (4b � 7v)2 23. (6n � 4p)2 24. (5q � 6s)2
25. (6a � 7b)(6a � 7b) 26. (8h � 3d)(8h � 3d) 27. (9x � 2y2)2
28. (3p3 � 2m)2 29. (5a2 � 2b)2 30. (4m3 � 2t)2
31. (6e3 � c)2 32. (2b2 � g)(2b2 � g) 33. (2v2 � 3e2)(2v2 � 3e2)
34. GEOMETRY Janelle wants to enlarge a square graph that she has made so that a sideof the new graph will be 1 inch more than twice the original side s. What trinomialrepresents the area of the enlarged graph?
GENETICS For Exercises 35 and 36, use the following information.In a guinea pig, pure black hair coloring B is dominant over pure white coloring b. Supposetwo hybrid Bb guinea pigs, with black hair coloring, are bred.
35. Find an expression for the genetic make-up of the guinea pig offspring.
36. What is the probability that two hybrid guinea pigs with black hair coloring will producea guinea pig with white hair coloring?
Practice Special Products
NAME ______________________________________________ DATE ____________ PERIOD _____
8-88-8
Reading to Learn MathematicsSpecial Products
NAME ______________________________________________ DATE ____________ PERIOD _____
8-88-8
© Glencoe/McGraw-Hill 501 Glencoe Algebra 1
Less
on
8-8
Pre-Activity When is the product of two binomials also a binomial?
Read the introduction to Lesson 8-8 at the top of page 458 in your textook.
What is a meant by the term trinomial product?
Reading the Lesson
1. Refer to the Key Concepts boxes on pages 458, 459, and 460.
a. When multiplying two binomials, there are three special products. What are the threespecial products that may result when multiplying two binomials?
b. Explain what is meant by the name of each special product.
c. Use the examples in the Key Concepts boxes to complete the table.
Symbols Product Example Product
Square of a Sum
Square of a Difference
Product of a Sum and a Difference
2. What is another phrase that describes the product of the sum and difference of two terms?
Helping You Remember
3. Explain how FOIL can help you remember how many terms are in the special productsstudied in this lesson.
© Glencoe/McGraw-Hill 502 Glencoe Algebra 1
Sums and Differences of Cubes Recall the formulas for finding some special products:
Perfect-square trinomials: (a � b)2 � a2 � 2ab � b2 or (a � b)2 � a2 � 2ab � b2
Difference of two squares: (a � b)(a � b) � a2 � b2
A pattern also exists for finding the cube of a sum (a � b)3.
1. Find the product of (a � b)(a � b)(a � b).
2. Use the pattern from Exercise 1 to evaluate (x � 2)3.
3. Based on your answer to Exercise 1, predict the pattern for the cube of a difference (a � b)3.
4. Find the product of (a � b)(a � b)(a � b) and compare it to your answer for Exercise 3.
5. Use the pattern from Exercise 4 to evaluate (x � 4)3.
Find each product.
6. (x � 6)3 7. (x � 10)3
8. (3x � y)3 9. (2x � y)3
10. (4x � 3y)3 11. (5x � 2)3
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
8-88-8
Chapter 8 Test, Form 1
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 503 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
1. Simplify y5 � y3.A. y2 B. y8 C. y15 D. 2y8 1.
2. Simplify (6x3)(x2).A. 6x5 B. 6x6 C. 7x5 D. 7x6 2.
3. Simplify (b4)3.A. b7 B. 3b4 C. b12 D. 3b7 3.
4. Simplify �aa
7
4�. Assume the denominator is not equal to zero.
A. a11 B. a28 C. a3 D. 1 4.
5. Simplify (5x2)(52x3).A. 25x6 B. 25x5 C. 125x6 D. 125x5 5.
6. Simplify ��2dc��3
. Assume the denominator is not equal to zero.
A. �6dc3
6� B. �
8dc� C. �
2d4
3c3� D. �
8dc3
3� 6.
7. Simplify �mm5
2nn
2
3�. Assume the denominator is not equal to zero.
A. m7n5 B. �mn
3� C. m3n D. �m
n3� 7.
8. Simplify (x2)(x�3)(x�2).
A. x�12 B. x7 C. �x13� D. �x
1�3� 8.
9. Express 3851 in scientific notation.A. 3.851 � 103 B. 38.51 � 102 C. 385.1 � 10 D. 3.851 � 10�3 9.
10. Express 5.9 � 103 in standard notation.A. 5900 B. 0.0059 C. 59,000 D. 0.00059 10.
11. Evaluate (3 � 104)(3 � 105).A. 6 � 109 B. 9 � 109 C. 6 � 1020 D. 9 � 1020 11.
12. Find the degree of the polynomial b5 � 2b3 � 7.A. 3 B. 8 C. 5 D. 7 12.
88
© Glencoe/McGraw-Hill 504 Glencoe Algebra 1
Chapter 8 Test, Form 1 (continued)
13. Which of the following polynomials shows the terms of x2 � 5x3 � 4 � 2xarranged so that the powers of x are in descending order?A. 5x3 � 2x � x2 � 4 B. �4 � 2x � x2 � 5x3
C. 5x3 � 4 � 2x � x2 D. 5x3 � x2 � 2x � 4 13.
14. MONEY Write a polynomial to represent the value of d dimes and nnickels.A. 10d � 5n B. 0.1d � 0.5n C. 0.1d � 0.05n D. d � n 14.
15. Find (n2 � 3n) � (2n2 � n).A. 3n2 � 2n B. 3n2 � 2n C. n2 � 4n D. n2 � 2n 15.
16. Find (2a � 5) � (3a � 1).A. 5a � 6 B. a � 4 C. �a � 6 D. �a � 4 16.
17. Find 3m2(2m2 � m).A. 5m4 � 3m3 B. 6m4 � 3m2 C. 5m4 � 3m D. 6m4 � 3m3 17.
18. Simplify 3(x2 � 2x) � x(x � 1).A. 4x2 � x B. 2x2 � 7x C. 2x2 � 3x D. 2x2 � 5x 18.
19. Solve 3(2n � 6) � �4(n � 3).
A. 3 B. �35� C. 6 D. 1�
45� 19.
20. Find (x � 3)(x � 5).A. x2 � 8x � 15 B. x2 � 15 C. 2x � 8 D. 2x � 15 20.
21. Find (2n � 3)(n � 4).A. 3n � 1 B. 2n2 � 12C. 2n2 � 5n � 12 D. 2n2 � 11n � 1 21.
22. Find (x � 3)(2x2 � 4x � 8).A. 2x3 � 10x2 � 20x � 24 B. 4x2 � 4x � 24C. 12x2 � 20x � 24 D. 2x3 � 2x2 � 4x � 24 22.
23. Find (y � 5)2.A. y2 � 25 B. 2y � 10 C. y2 � 10y � 10 D. y2 � 10y � 25 23.
24. Find (3y � 1)2.A. 6y2 � 6y � 1 B. 9y2 � 6y � 1 C. 9y2 � 3y � 1 D. 9y2 � 6y � 1 24.
25. Find (2x � 5)(2x � 5).A. 4x B. 4x2 � 25 C. 4x2 � 20x � 25 D. 4x2 � 25 25.
Bonus Simplify (3n�1)(32n)4. B:
NAME DATE PERIOD
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Chapter 8 Test, Form 2A
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 505 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
1. Simplify (9d4)(�6d5).A. 3d9 B. 3d C. �54d9 D. �54d20 1.
2. Simplify (x3)8.A. x24 B. x11 C. 8x24 D. 8x11 2.
3. Simplify (�2hk)4(4h3k5)2.A. 2h24k40 B. �64h9k11 C. � 256h10k14 D. 256h10k14 3.
4. Simplify �aa
9
3�. Assume the denominator is not equal to zero.
A. a3 B. a12 C. a6 D. a27 4.
5. Simplify �93b6
�b4
1cc2
5�. Assume the denominator is not equal to zero.
A. �27
c3b4� B. �
4cb3
4� C. �
27c3b3� D. �
4cb3
5� 5.
6. Simplify �((y3
2yn4n
�
6
3))2
4�. Assume the denominator is not equal to zero.
A. �y916� B. �n
924� C. 9y16 D. 9n24 6.
7. Express 4173 in scientific notation.A. 4.173 � 103 B. 41.73 � 102 C. 417.3 � 10 D. 4.173 � 10�3 7.
8. Evaluate (4 � 10�2)(2 � 108).A. 8 � 10�16 B. 8 � 106 C. 6 � 106 D. 6 � 10�16 8.
9. Find the degree of the polynomial 3xy � 8x2y5 � x7y.A. 2 B. 7 C. 8 D. 10 9.
10. Arrange the terms of 4x3y2 � 6xy3 � 2x5 � 3y so that the powers of x are in descending order.A. 3y � 6xy3 � 4x3y2 � 2x5 B. 4x3y2 � 3y � 2x5 � 6xy3
C. 2x5 � 4x3y2 � 6xy3 � 3y D. �6xy3 � 4x3y2 � 3y � 2x5 10.
11. Find (9t2 � 4t � 6) � (t2 � 2t � 4).A. 8t2 � 6t � 10 B. 8t2 � 2t � 2 C. 9t2 � 6t � 2 D. 9t2 � 6t � 10 11.
88
© Glencoe/McGraw-Hill 506 Glencoe Algebra 1
Chapter 8 Test, Form 2A (continued)
12. CARS The number of domestic car sales from 1981–1999 in millions is modeled by the expression y � �0.01n2 � 0.11n � 6.51 where n is the number of years since 1981. The number of import car sales from 1981–1999 in millions is modeled by the expression y � 0.02n � 2.57. Find an expression that models the total number of car sales n years since 1981.A. �0.01n2 � 0.09n � 3.94 B. 0.01n2 � 0.13n � 9.08C. �0.01n2 � 0.31n � 8.08 D. �0.01n2 � 0.13n � 9.08 12.
13. Simplify 2a2(5a � 6) � 5a(a2 � 3a � 4) � 7(a � 5).A. 5a3 � 3a2 � 27a � 35 B. 5a3 � 27a2 � 13a � 35C. 5a3 � 10a � 7 D. none of these 13.
14. Find (c � 5)(c � 7).A. c2 � 12c � 35 B. c2 � 12c � 35C. c2 � 12c � 35 D. c2 � 35 14.
15. Find (3y � 4)(2y2 � y � 1).A. 6y3 � 5y2 � 7y � 4 B. 6y3 � 5y2 � 7y � 4C. 6y3 � 7y2 � 7y � 4 D. 6y3 � 5y2 � 7y � 4 15.
16. Find (3a � 2b)(3a � 2b).A. 9a2 � 4b2 B. 9a2 � 4b2
C. 9a2 � 12ab � 4b2 D. 9a2 � 12ab � 4b2 16.
17. Find (4a2 � b)2.A. 16a4 � b2 B. 8a4 � b2
C. 16a4 � 8a2b � b2 D. 4a4 � 8a2b � b2 17.
18. Solve 6(n � 11) � 12 � 4(2n � 3).A. �11 B. 11 C. �33 D. 33 18.
19. Solve 5x2 � 3x � (7x2 � 5x) � (2x2 � 16).A. 2 B. �2 C. 8 D. �8 19.
20. GEOMETRY The length of a rectangle is 4 units less than twice the width.If the length is decreased by 3 units and the width is increased by 1 unit,the area is decreased by 16 square units. If w is the original width, which equation must be true?A. (2w � 3)(w � 3) � w(2w � 4) � 16B. 2(2w � 3) � 2(w � 3) � 2w � 2(2w � 4) � 16C. (2w � 7)(w � 1) � w(2w � 4) � 16D. 2(2w � 7) � 2(w � 1) � 2w � (2w � 4) � 16 20.
Bonus Simplify �773
x
x
�
�
3
1�. B:
NAME DATE PERIOD
88
Chapter 8 Test, Form 2B
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 507 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
1. Simplify (5d3)( � 2d2).A. 10d5 B. �10d5 C. 10d6 D. �10d6 1.
2. Simplify (m4)2.A. 6m B. m8 C. m6 D. 2m4 2.
3. Simplify (�2xy2)4(2x3y4)2.A. 4x24y32 B. �8x9y6 C. 64x10y16 D. �4x10y16 3.
4. Simplify �aa1
4
2�. Assume the denominator is not equal to zero.
A. a3 B. a16 C. a48 D. a8 4.
5. Simplify �26nn�
�
1y3
�y
3�. Assume the denominator is not equal to zero.
A. �4ny2
3� B. �
3ny2
4� C. �n4
3y2� D. �
3yn4
2� 5.
6. Simplify �((aa�
4
2
bb�
4
8))�
3
6�. Assume the denominator is not equal to zero.
A. ab3 B. 1 C. �ab4
2
8
4� D. �a
b4
2
8
4� 6.
7. Express 5.43 � 10�4 in standard notation.A. 54,300 B. 0.00543 C. 5430 D. 0.000543 7.
8. Evaluate �22..488
��10
1�03
7�.
A. 0.48 � 10�4 B. 1.2 � 10�4 C. 1.2 � 1010 D. 0.48 � 1010 8.
9. Find the degree of the polynomial 2x3y � 4xy2 � 9x3y2.A. 4 B. 3 C. 12 D. 5 9.
10. Arrange the terms of x2y3 � 4xy2 � 3x3y � 6 so that the powers of x are in ascending order.A. 6 � 4xy2 � x2y3 � 3x3y B. x2y3 � 3x3y � 4xy2 � 6C. 6 � 4xy2 � 3x3y � x2y3 D. 6 � 3x3y � 4xy2 � x2y3 10.
11. Find (3c2 � 8c � 5) � (c2 � 8c � 6).A. 3c2 � 1 B. 4c2 � 11 C. 4c2 � 16c � 1 D. 2c2 � 16c � 1 11.
88
© Glencoe/McGraw-Hill 508 Glencoe Algebra 1
Chapter 8 Test, Form 2B (continued)
12. CLUBS The number of girls in a local 4-H club is modeled by the expression 4n2 � n � 52 where n is the number of years after 1990. The number of girls in 4H who are age 8 and under is modeled by the expression n2 � 13.Find an expression that models the number of girls older than 8 in the club.A. 3n2 � n � 39 B. 3n2 � n � 39C. �3n2 � n � 39 D. �3n2 � n � 39 12.
13. Simplify 3b2(4b � 7) � 2b(b2 � 5b � 3) � 6(b � 2).A. 14b3 � 11b2 � 12b � 12 B. 41b2 � 12C. 14b3 � 31b2 � 12b � 12 D. 10b3 � 31b2 � 12 13.
14. Find (x � 2)(x � 4).A. x2 � 8 B. x2 � 2x � 6C. x2 � 2x � 8 D. x2 � 6x � 8 14.
15. Find (3x � 2)(4x2 � 2x � 7).A. 12x3 � 2x2 � 25x � 14 B. 12x3 � 14x2 � 25x � 14C. 7x3 � 9x2 � 25x � 14 D. 7x3 � 7x2 � 4x � 5 15.
16. Find (3y � 4z)(3y � 4z).A. 9y2 � 16z2 B. 9y2 � 24yz � 16z2
C. 9y2 � 16z2 D. 9y2 � 24yz � 16z2 16.
17. Find (�2r2 � s)2.A. 4r4 � s2 B. 4r4 � 4r2s � s2
C. �4r4 � s2 D. �4r4 � 4r2s � s2 17.
18. Solve �4(5 � 2n) � 8( � 6 � 5n).
A. ��19� B. ��
238� C. ��
78� D. ��1
72�
18.
19. Solve x(x � 3) � 2 � 2 � x(x � 1).A. 2 B. �2 C. 1 D. 0 19.
20. ART A picture is 4 inches longer than it is wide. It is surrounded by a mat that is 2 inches wide. The total area of the mat is 112 square inches. If wis the width of the picture, which equation is true?A. (w � 4)(w � 8) � w(w � 4) � 112B. (w � 2)(w � 6) � w(w � 4) � 112C. (w � 4)(w � 8) � w(w � 4) � 112D. (w � 2)(w � 6) � w(w � 4) � 112 20.
Bonus Simplify 32n�1 � 35n. B:
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88
Chapter 8 Test, Form 2C
© Glencoe/McGraw-Hill 509 Glencoe Algebra 1
Simplify.
1. 3y5 � y3 1.
2. (9m3n5)(�2mn2) 2.
3. (w5y4)3 3.
4. 4a3n6 � 4(a3n)6 � 4(an2)3 4.
For Questions 5–7, simplify. Assume that no denominator is equal to zero.
5. �pp6
3qq2
� 5.
6. �146rr�
3
1ss�
2
5� 6.
7. �(�
(48xx3
2
yy)2
3)2
� 7.
8. Express 0.000498 in scientific notation. 8.
9. Express 1.27 � 105 in standard notation. 9.
For Questions 10 and 11, express each result in scientific and standard notation.
10. Evaluate (2.5 � 10�2)(4 � 106). 10.
11. The radius of Earth is approximately 2.51 � 108 inches. The 11.radius of the Sun is approximately 2.74 � 1010 inches. How many times greater is the radius of the Sun than the radius of Earth?
12. Find the degree of the polynomial 2x3y3 � 4xy � 10x3y. 12.
13. Arrange the terms of the polynomial 4 � 3x3y3 � x5y � xy so 13.that the powers of x are in descending order.
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Ass
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© Glencoe/McGraw-Hill 510 Glencoe Algebra 1
Chapter 8 Test, Form 2C (continued)
Find each sum or difference.
14. (5n2 � 2ny � 3y2) � (9n2 � 8ny � 10y2) 14.
15. (11m2 � 2mn � 8n2) � (8m2 � 4mn � 2n2) 15.
16. (x2 � 5y) � (2x2 � 6y) 16.
Find each product.
17. 5hk2(2h2k � hk3 � 4h2k2) 17.
18. (4x2 � 2y2)(2x2 � y2) 18.
19. (3s � 5)(2s2 � 8s � 6) 19.
20. (5c � 4)2 20.
21. (7a � 3b)(7a � 3b) 21.
22. (4n � 1)2 22.
For Questions 23 and 24, solve each equation.
23. �6(3n � 2) � 4(�3 � 2n) 23.
24. 8n � 11 � 4 � 5(2n � 1) 24.
25. GARDENING The length of a rectangular garden is 8 feet 25.longer than the width. The garden is surrounded by a 4-foot sidewalk. The sidewalk has an area of 320 square feet.Find the dimensions of the garden.
Bonus If you multiply (x � 1)20, how many terms will there B:be? (Hint: Look for a pattern in the smaller powers of (x � 1).)
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88
Chapter 8 Test, Form 2D
© Glencoe/McGraw-Hill 511 Glencoe Algebra 1
Simplify.
1. 5x4 � x3 1.
2. (3a2b5)(�2ab3) 2.
3. (w3z7)3 3.
4. 4a4b8 � 2(ab2)4 � 4(a2b4)2 4.
For Questions 5–7, simplify. Assume that no denominator is equal to zero.
5. ��
41m2m
5
3� 5.
6. �48bb
�
2d3
�d2
5� 6.
7. �(�(3
3rr3
2ss5
7)3
)2� 7.
8. Express 12,556 in scientific notation. 8.
9. Express 7.43 � 10�3 in standard notation. 9.
For Questions 10 and 11, express each result in scientific and standard notation.
10. The minimum distance from Earth to the Moon is 10.approximately 2.26 � 105 miles. There are approximately 6.34 � 104 inches in one mile. What is the minimum distance from Earth to the Moon in inches?
11. �25.7.4
��
1100�
4
3� 11.
12. Find the degree of the polynomial 2x2y � 4x5 � 6xy3. 12.
13. Arrange the terms of the polynomial 3x2y � xy2 � 3y3 � x3 13.so that the powers of x are in descending order.
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© Glencoe/McGraw-Hill 512 Glencoe Algebra 1
Chapter 8 Test, Form 2D (continued)
Find each sum or difference.
14. (7m2 � 3m � 4) � (3m2 � 9m � 5) 14.
15. (4y2 � 3y � 7) � (4y2 � 7y � 2) 15.
16. (3a3 � 4b) � (2a3 � b) 16.
Find each product.
17. 3x2y(2x2y � 5xy2 � 8y3x2) 17.
18. (3r2 � 5s2)(3r2 � 5s2) 18.
19. (2n � 3)(3n2 � 4n � 1) 19.
20. (5y � 6)2 20.
21. (2k � 5r)(2k � 5r) 21.
22. (2c � 1)2 22.
For Questions 23 and 24, solve each equation.
23. 5x � 8 � 3 � 2(3x � 4) 23.
24. �5(2n � 3) � 7(3 � n) 24.
25. GARDENING The length of a rectangular garden is 5 feet 25.longer than its width. The garden is surrounded by a 2-foot-wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden.
Bonus If (x � 1)10 is multiplied out, how many terms will there B:be? (Hint: Look for a pattern in the smaller powers of (x � 1).)
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88
Chapter 8 Test, Form 3
© Glencoe/McGraw-Hill 513 Glencoe Algebra 1
Simplify.
1. (ab8)(3a6b2) 1.
2. ��23�h3�4
2.
3. ��23�r�3
(27r)(5s)2��12�s4�3
3.
4. (43x�7)(42x�9) 4.
For Questions 5–7, simplify. Assume that no denominator is equal to zero.
5. ��
95c46cd2
2d5
� 5.
6. �(�82mm
�x�
5x3
0)�4
� 6.
7. ���63aa3
2
bb�
�
4
3��2��4�a
5�b3���3
7.
8. Express 196,783 in scientific notation. 8.
For Questions 9 and 10, express each result in scientific and standard notation.
9. (7.2 � 10�3)(8.1 � 10�2) 9.
10. �4.55.91
��
1100
�
2
3� 10.
11. Arrange the terms of the polynomial 2xy � 6 � 4x5y2 � 7x6y3 11.so that the powers of x are in descending order.
12. Find the degree of the polynomial m2np2 � mn3p2 � 4m4n. 12.
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Ass
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ent
© Glencoe/McGraw-Hill 514 Glencoe Algebra 1
Chapter 8 Test, Form 3 (continued)
For Questions 13 and 14, find each sum or difference.
13. (8w2 � 4w � 2) � (2w2 � w � 6) 13.
14. (7u2v � 3uv � 4uv2) � (4uv � 3u2v � 2uv2) 14.
15. GEOMETRY The measures of two sides 15.of a triangle are given on the triangle at the right. If the perimeter of the triangle is 6x2 � 8y, find the measure of the third side.
16. Simplify 5n2(n � 6) � 2n(3n2 � n � 6) � 7(n2 � 3). 16.
For Questions 17–20, find each product.
17. (2y � 7)(4y � 4) 17.
18. ��23�m � 1���
12�m � 2� 18.
19. (4x � y)(2x2 � xy � 5y2) 19.
20. (5r2 � 3s2)(5r2 � 3s2) 20.
21. A square has sides of length (3x � 1) feet. Write an 21.expression that represents the area of the square.
22. Solve y(y � 6) � (5y2 � 36) � (4y2 � 3y). 22.
23. If f(x) � x2 � 5x and g(x) � 2x � x2, find f(a � 1) � g(a � 1). 23.
24. If a2 � b2 � 11 and ab � 3, find the value of (a � b)2. 24.
25. GEOMETRY The length of a rectangle is 4 centimeters 25.more than its width. If the length is increased by 8 centimeters and the width is decreased by 4 centimeters,the area will remain unchanged. Find the original dimensions of the rectangle.
Bonus Graph the solution set of B:(x � 3)(x � 5) � (x � 1)2 � 2(x � 1).
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88
x2 � y
2x2 � x � 5y
Chapter 8 Open-Ended Assessment
© Glencoe/McGraw-Hill 515 Glencoe Algebra 1
Demonstrate your knowledge by giving a clear, concise solutionto each problem. Be sure to include all relevant drawings andjustify your answers. You may show your solution in more thanone way or investigate beyond the requirements of the problem.
1. For each equation determine why the statement is incorrect.Explain how to change the right side of the equation to make a true statement.a. (4u � 5v) � (u � v) � 3u � 4vb. x2y(3x3 � 4) � 3x6y � 4x2yc. (3a � 5b)2 � 9a2 � 25b2
2. a. State whether the number 23.4 � 108 is in scientific notation.Explain how you determined your answer.
b. Explain why scientific notation is helpful when dividing22,100,000 by 0.00000013. Find the quotient 22,100,000 0.00000013.
3. Give a counterexample for each statement.a. The degree of a polynomial is always 2 or greater.b. The degree of a trinomial is always greater than the degree
of a monomial.
4. a. Simplify ��24aa�3
2��4by using the Quotient of Powers property
first, then use the Power of a Power property.
b. Simplify ��24aa�3
2��4by using the Power of a Quotient property
first, then use the Quotient of Powers property.c. Write a statement that generalizes the results of part a
and part b.
5. Draw an area model demonstrating the product (3x � y)(x � 2y).Find the product algebraically. Explain how the algebraic productverifies the area model.
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© Glencoe/McGraw-Hill 516 Glencoe Algebra 1
Chapter 8 Vocabulary Test/Review
Write the letter of the term that best matches each statement or phrase.
1. constant
2. Power of a Power
3. Product of Powers
4. FOIL method
5. Quotient of Powers
6. Power of a Quotient
7. monomial
8. zero exponent
9. trinomial
10. binomial
In your own words—Define each term.
11. degree of a monomial
12. degree of a polynomial
13. scientific notation
binomialconstantdegree of a monomialdegree of a polynomialdifference of squaresFOIL method
monomialnegative exponentpolynomialPower of a PowerPower of a ProductProduct of Powers
Power of a QuotientQuotient of Powersscientific notationtrinomialzero exponent
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a. property that tells us to find the power ofthe numerator and the power of thedenominator
b. property that tells us that any nonzeronumber raised to the zero power is 1
c. property that tells us to multiplyexponents
d. the sum of three monomials
e. monomials that are real numbers
f. used to multiply two binomials
g. property that tell us to add exponentswhen multiplying two powers that havethe same base
h. the sum of two monomials
i. property that tells us to subtractexponents when dividing two powers thathave the same base
j. a number, a variable, or a product of anumber and one or more variables
Chapter 8 Quiz (Lessons 8–1 and 8–2)
88
© Glencoe/McGraw-Hill 517 Glencoe Algebra 1
Simplify.
1. (r3)(2r5) 2. (x5)4
3. (�4m2n3)(3mn4) 4. (�5x4y2)3
5. (2cd)2(�4c3)2 6. (5y2w4)2 � 2(yw2)4
Simplify. Assume that no denominator is equal to zero.
7. �661
9
5� 8. �
yy
8
3� 9. �rr6
4nn�
2
7�
10. STANDARDIZED TEST PRACTICE Write the ratio of the area of a circle with radius r to the circumference of the same circle.
A. �2r� B. 2 C. �2
r� D. �2
1r�
10.
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Chapter 8 Quiz (Lessons 8–3 and 8–4)
For Questions 1 and 2, express each number in scientific notation.
1. 57,600 2. 0.0000061
3. Express 6.4871 � 10�3 in standard notation.
Evaluate. Express each result in scientific and standard notation.
4. �74.2.5
��
1100�
2
5� 5. (3.5 � 106)(8.2 � 103)
Find the degree of each polynomial.
6. 5a � 2b2 � 1 7. 24xy � xy3 � x2
For Questions 8 and 9, arrange the terms of each polynomial so that the powers of x are in descending order.
8. 4x2 � 3x3 � 2x � 12 8.
9. 5x3y � 3xy4 � x2y3 � y4 9.
10. Arrange the terms of the polynomial �3 � x2 � 4x so that 10.the powers of x are in ascending order.
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1.
2.
3.
4.
5.
6.
7.
8.
9.
1.
2.
3.
4.
5.
6.
7.
© Glencoe/McGraw-Hill 518 Glencoe Algebra 1
For Questions 1 and 2, find each sum or difference.
1. (�2x2 � x � 6) � (5x2 � 4x � 2) 1.
2. (5a � 9b) � (2a � 4b) 2.
3. Find 3xy(2x2 � 5xy � 7y2). 3.
4. Simplify 5c2(c � 10) � 4c(2c2 � 6c � 1). 4.
5. Solve 3(2p � 1) � 7(5 � p) � 6. 5.
Chapter 8 Quiz (Lesson 8–7)
Find each product.
1. (4m � 1)(m � 2) 1.
2. (2c � 3)(c2 � 4c � 5) 2.
3. (4h � 3)2 3.
4. (a � 9)2 4.
5. (2x � 6y)(2x � 6y) 5.
6. (m2 � 2n)2 6.
7. (9x � 7)(9x � 7) 7.
8. (a � 3b)(a � 3b) 8.
For Exercises 9 and 10, use the figure.
9. Write an expression to represent the area of the top side of 9.the prism.
10. Write an expression to represent the volume of the prism. 10.
4a � 4a � 1
a � 3
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Chapter 8 Quiz (Lessons 8–5 and 8–6)
88
NAME DATE PERIOD
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88
Chapter 8 Mid-Chapter Test (Lessons 8–1 through 8–4)
© Glencoe/McGraw-Hill 519 Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
1. Simplify (n5)(n2)(m3)(m4).A. n10m12 B. n7m7 C. nm7 D. nm14 1.
2. Simplify (3w2v)2( � 2w5v2)3.A. �72w19v8 B. 72w12v7 C. �36w32v10 D. 36w19v6 2.
For Questions 3 and 4, simplify. Assume the denominator is not equal to zero.
3. �mm
6
2nn
3
6�
A. �mn3
4� B. ��
mn3
4� C. ��
mn3
8� D. �
mn3
8� 3.
4. �((zz2
3ww
�
2
1
))2
3�
A. �w1
7� B. �zw1
7
2� C. w D. �w
1� 4.
5. Express 31,000,000 in scientific notation.A. 31 � 106 B. 3.1 � 10�7
C. 3.1 � 107 D. 31 � 10�6 5.
6. Find the degree of the polynomial 4x2y3 � 2xy2 � 5x3y.A. 4 B. 3 C. 6 D. 5 6.
7. Express 4.02 � 10�3 in standard notation.A. 0.00402 B. 402,000 C. 4020 D. 402 7.
Evaluate. Express each result in scientific and standard notation.
8. �15.1
�7 �
101�01
2� 9. (8.3 � 102)(9.1 � 10�7)
For Questions 10 and 11, simplify. Assume that no denominator is equal to zero.
10. �52(xx4
3
yy2
5
)3� 11. ��1
�41m0m
�7
�
y1
�y3
0
rr�4�
12. Find the degree of 5c2 � 3c4 � 2c3 � 1. 12.
Arrange the terms of each polynomial so that the powers of x are in descending order. 13.
13. 6 � 2x2 � 3x � 4x3
14. 2a2x3 � 8x4 � 3a4x2 � 8x 14.
Part II
Part I
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Ass
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8.
9.
10.
11.
© Glencoe/McGraw-Hill 520 Glencoe Algebra 1
Chapter 8 Cumulative Review (Chapters 1–8)
1. Find a counterexample for the conditional statement. 1.If a number is divisible by 5, then the one’s digit is a 5.(Lesson 1-7)
2. Solve a(b � c) � �ab� for c. (Lesson 3-8) 2.
3. Write an equation in function 3.notation for the relation.(Lesson 4-8)
4. TUITION The average cost of tuition and fees at a four-year 4.college was $3,356 for the year 1999–2000. For the year 1997–1998 the average cost was $3,111. Find the rate of change between the year 1997–1998 and the year 1999–2000. (Lesson 5-1)
5. Write y � 1 � 4(x � 2) in slope intercept form. (Lesson 5-5) 5.
6. Solve 14u � 9 � 10u 21. (Lesson 6-3) 6.
7. Solve 3y � 4 � 7. (Lesson 6-5) 7.
8. RECREATION Barrington needs to buy snorkels and fins for 8.his family for their annual beach vacation. Snorkels cost $8 a set and fins cost $12 a pair. Write an inequality that represents this situation if Barrington has $62 to spend. (Lesson 6-6)
9. Graph the system of equations. Then determine whether 9.
the system has no solution, one solution, or infinitely manysolutions. If the system has one solution, name it. (Lesson 7-1)
x � y � 4y � x
10. Determine the best method to solve the system of equations.Then solve the system. (Lesson 7-4)
5x � 2y � 72x � 5y � �3 10.
11. Simplify �5117x�
x2
1
yy3
�. Assume the denominator is not equal to
zero. (Lesson 8-2) 11.
12. Evaluate (6 � 105)(2.3 � 103). Express the result in 12.scientific and standard notation. (Lesson 8-3)
13. Find ��23�a2 � �
14�a � �
15�� � ��
13�a2 � �
34�a � �
25��. (Lesson 8-5) 13.
14. Find (3x � 2)2. (Lesson 8-8) 14.
y
xO
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y
xO
Standardized Test Practice (Chapters 1–8)
© Glencoe/McGraw-Hill 521 Glencoe Algebra 1
1. Write y � 11 � �12�(x � 12) in standard form. (Lesson 5-5)
A. y � �12�x � 5 B. y � �
12�x � 17 C. x � 2y � �10 D. x � 2y � 17 1.
2. Ashanti wants to collect more than 50 food items for the local homeless shelter. If he has already collected 13, how many more items must he collect? (Lesson 6-1)
E. 37 F. at least 38 G. at least 37 H. more than 36 2.
3. Solve �5n � 22 � �73. (Lesson 6-3)
A. {n � n � 19} B. {n � n � 19} C. �n � n � ��551�� D. {n � n � 90} 3.
4. Solve � 5k � 2 � 1. (Lesson 6-5)
E. �k � k � ��35� or k ��
15�� F. �k � k � �
35� � k � �
15��
G. H. {k � k is a real number.} 4.
5. Use substitution to solve the system of equations. (Lesson 7-2)
y � �2x5x � 3y � 4A. (�4, 8) B. (8, �4) C. (�8, 4) D. (4, �8) 5.
6. Use elimination to solve the system of equations. (Lesson 7-3)
x � 3y � �62x � 3y � �9E. (�2, �4) F. (�6, 1) G. (�3, �1) H. (3, �5) 6.
7. Simplify �(3(�32
2))((33
3
�)3)�. (Lesson 8-2)
A. 310 B. 312 C. �1 D. �13� 7.
8. Express 0.46 � 103 in scientific notation. (Lesson 8-3)
E. 0.46 � 103 F. 4.6 � 102 G. 4.6 � 103 H. 46 � 101 8.
9. Find (3n2 � 6n) � (5n3 � 2n) � (2n3 � n2). (Lesson 8-5)
A. 3n3 � 2n2 � 8n B. 6n3 � n2 � 4nC. 3n3 � 4n2 � 4n D. 6n3 � 4n2 � 8n 9.
10. Find (7b � 11)(b � 3). (Lesson 8-7)
E. 7b2 � 10b � 33 F. 7b2 � 11b � 33G. 7b2 � 11b � 8 H. 7b2 � 10b � 8 10. HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
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Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
© Glencoe/McGraw-Hill 522 Glencoe Algebra 1
Standardized Test Practice (continued)
11. Evaluate 4x(y2 � z2) if x � 3, y � 5 and z � 4. 11. 12.(Lesson 1-2)
12. After receiving his allowance, Spencer spent half of his money on a card for his mother.He bought 2 toy cars for $0.98 to give to his brothers, and a soft drink for $0.35. How much did Spencer receive for his allowance if he has $0.42 left over? (Lesson 3-4)
13. At the end of the 2001 football season, the 13. 14.Dallas Cowboys and the Denver Broncos had won a total of 7 Super Bowls. The Cowboys had won 2.5 times as many Super Bowls as the Broncos. How many Super Bowls had the Dallas Cowboys won? (Lesson 7-2)
14. Express 5.7 � 10�2 in standard notation.(Lesson 8-3)
Column A Column B
15. 15.
(Lesson 2-7)
16. y � 3x � 10 16.y � �2x � 15.
(Lesson 7-2)
17. 17.
(Lesson 8-4)
DCBAthe degree of3x2y2 � 6x2y3 � 8x3y2
the degree of7x5 � 4x3 � x6
yx
DCBA
DCBA
��191����
57
��
Part 3: Quantitative Comparison
Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.
0 0 0
.. ./ /
.
99 9 987654321
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87654321
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0 0 0
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.
99 9 987654321
87654321
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87654321
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.
99 9 987654321
87654321
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0 0 0
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.
99 9 987654321
87654321
87654321
87654321
NAME DATE PERIOD
88
NAME DATE PERIOD
Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
A
D
C
B
Standardized Test PracticeStudent Record Sheet (Use with pages 470–471 of the Student Edition.)
© Glencoe/McGraw-Hill A1 Glencoe Algebra 1
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7 9
2 5 8 10
3 6
Solve the problem and write your answer in the blank.
For Questions 11 and 13, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.
11 (grid in) 11 13
12
13 (grid in)
14
15
16
Select the best answer from the choices given and fill in the corresponding oval.
17 21
18 22
19 23
20
Record your answers for Question 24 on the back of this paper.
DCBA
DCBADCBA
DCBADCBA
DCBADCBA
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
DCBADCBA
DCBADCBADCBADCBA
DCBADCBADCBADCBA
NAME DATE PERIOD
88
An
swer
s
Part 3 Quantitative ComparisonPart 3 Quantitative Comparison
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 4 Open-EndedPart 4 Open-Ended
Part 1 Multiple ChoicePart 1 Multiple Choice
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Mu
ltip
lyin
g M
on
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-1
8-1
©G
lenc
oe/M
cGra
w-H
ill45
5G
lenc
oe A
lgeb
ra 1
Lesson 8-1
Mu
ltip
ly M
on
om
ials
A m
onom
ial
is a
nu
mbe
r,a
vari
able
,or
a pr
odu
ct o
f a
nu
mbe
ran
d on
e or
mor
e va
riab
les.
An
exp
ress
ion
of
the
form
xn
is c
alle
d a
pow
eran
d re
pres
ents
the
prod
uct
you
obt
ain
wh
en x
is u
sed
as a
fac
tor
nti
mes
.To
mu
ltip
ly t
wo
pow
ers
that
hav
eth
e sa
me
base
,add
th
e ex
pon
ents
.
Pro
du
ct o
f P
ow
ers
For
any
num
ber
aan
d al
l int
eger
s m
and
n, a
m�
an�
am
� n
.
Sim
pli
fy (
3x6 )
(5x2
).
(3x6
)(5x
2 ) �
(3)(
5)(x
6�
x2)
Ass
ocia
tive
Pro
pert
y
�(3
�5)
(x6
� 2
)P
rodu
ct o
f P
ower
s
�15
x8S
impl
ify.
Th
e pr
odu
ct i
s 15
x8.
Sim
pli
fy (
�4a
3 b)(
3a2 b
5 ).
(�4a
3 b)(
3a2 b
5 )�
(�4)
(3)(
a3�
a2)(
b�
b5)
��
12(a
3 �
2)(
b1 �
5)
��
12a5
b6
Th
e pr
odu
ct i
s �
12a5
b6.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sim
pli
fy.
1.y(
y5)
2.n
2�
n7
3.(�
7x2 )
(x4 )
y6
n9
�7x
6
4.x(
x2)(
x4)
5.m
�m
56.
(�x3
)(�
x4)
x7m
6x7
7.(2
a2)(
8a)
8.(r
s)(r
s3)(
s2)
9.(x
2 y)(
4xy3
)
16a3
r2s6
4x3 y
4
10.
(2a3
b)(6
b3)
11.(
�4x
3 )(�
5x7 )
12.(
�3j
2 k4 )
(2jk
6 )
4a3 b
420
x10
�6j
3 k10
13.(
5a2 b
c3) �
abc4�
14.(
�5x
y)(4
x2)(
y4)
15.(
10x3
yz2 )
(�2x
y5z)
a3b
2 c7
�20
x3 y
5�
20x
4 y6 z
3
1 � 5
1 � 3
©G
lenc
oe/M
cGra
w-H
ill45
6G
lenc
oe A
lgeb
ra 1
Pow
ers
of
Mo
no
mia
lsA
n e
xpre
ssio
n o
f th
e fo
rm (
xm)n
is c
alle
d a
pow
er o
f a
pow
eran
d re
pres
ents
th
e pr
odu
ct y
ou o
btai
n w
hen
xm
is u
sed
as a
fac
tor
nti
mes
.To
fin
d th
epo
wer
of
a po
wer
,mu
ltip
ly e
xpon
ents
.
Po
wer
of
a P
ow
erF
or a
ny n
umbe
r a
and
all i
nteg
ers
man
d n
, (a
m)n
�am
n.
Po
wer
of
a P
rod
uct
For
any
num
ber
aan
d al
l int
eger
s m
and
n,
(ab)
m�
amb
m.
Sim
pli
fy (
�2a
b2)3
(a2 )
4 .
(�2a
b2)3
(a2 )
4�
(�2a
b2)3
(a8 )
Pow
er o
f a
Pow
er
�(�
2)3 (
a3)(
b2)3
(a8 )
Pow
er o
f a
Pro
duct
�(�
2)3 (
a3)(
a8)(
b2)3
Com
mut
ativ
e P
rope
rty
�(�
2)3 (
a11 )
(b2 )
3P
rodu
ct o
f P
ower
s
��
8a11
b6P
ower
of
a P
ower
Th
e pr
odu
ct i
s �
8a11
b6.
Sim
pli
fy.
1.(y
5 )2
2.(n
7 )4
3.(x
2 )5 (
x3)
y10
n28
x13
4.�
3(ab
4 )3
5.(�
3ab4
)36.
(4x2
b)3
�3a
3 b12
�27
a3 b
1264
x6 b
3
7.(4
a2)2
(b3 )
8.(4
x)2 (
b3)
9.(x
2y4
)5
16a4
b3
16x
2 b3
x10 y
20
10.(
2a3 b
2 )(b
3 )2
11.(
�4x
y)3 (
�2x
2 )3
12.(
�3j
2 k3 )
2 (2j
2 k)3
2a3 b
851
2x9 y
372
j10 k
9
13.(
25a2
b)3 �
abc �2
14.(
2xy)
2 (�
3x2 )
(4y4
)15
.(2x
3 y2 z
2 )3 (
x2z)
4
625a
8 b5 c
2�
48x
4 y6
8x17
y6 z
10
16.(
�2n
6 y5 )
(�6n
3 y2 )
(ny)
317
.(�
3a3 n
4 )(�
3a3 n
)418
.�3(
2x)4
(4x5
y)2
12n
12y1
0�
243a
15n
8�
768x
14y
2
1 � 5Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Mu
ltip
lyin
g M
on
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-1
8-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 8-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Mu
ltip
lyin
g M
on
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-1
8-1
©G
lenc
oe/M
cGra
w-H
ill45
7G
lenc
oe A
lgeb
ra 1
Lesson 8-1
Det
erm
ine
wh
eth
er e
ach
exp
ress
ion
is
a m
onom
ial.
Wri
te y
esor
no.
Exp
lain
.
1.11
Yes;
11 is
a r
eal n
um
ber
an
d a
n e
xam
ple
of
a co
nst
ant.
2.a
�b
No
;Th
is is
th
e d
iffe
ren
ce,n
ot
the
pro
du
ct,o
f tw
o v
aria
ble
s.
3.N
o;T
his
is t
he
qu
oti
ent,
no
t th
e p
rod
uct
,of
two
var
iab
les.
4.y
Yes;
Sin
gle
var
iab
les
are
mo
no
mia
ls.
5.j3
kYe
s;T
his
is t
he
pro
du
ct o
f tw
o v
aria
ble
s.
6.2a
�3b
No
;Th
is is
th
e su
m o
f tw
o m
on
om
ials
.
Sim
pli
fy.
7.a2
(a3 )
(a6 )
a11
8.x(
x2)(
x7)
x10
9.(y
2 z)(
yz2 )
y3z3
10.(
�2 k2 )
(�3 k
)�5 k
3
11.(
e2f4
)(e2
f2)
e4f6
12.(
cd2 )
(c3 d
2 )c4
d4
13.(
2x2 )
(3x5
)6x
714
.(5a
7 )(4
a2)
20a9
15.(
4xy3
)(3x
3 y5 )
12x
4 y8
16.(
7a5 b
2 )(a
2 b3 )
7a7 b
5
17.(
�5m
3 )(3
m8 )
�15
m11
18.(
�2c
4 d)(
�4c
d)
8c5 d
2
19.(
102 )
310
6o
r 1,
000,
000
20.(
p3)1
2p
36
21.(
�6p
)236
p2
22.(
�3y
)3�
27y
3
23.(
3pq2
)29p
2 q4
24.(
2b3 c
4 )2
4b6 c
8
GEO
MET
RYE
xpre
ss t
he
area
of
each
fig
ure
as
a m
onom
ial.
25.
26.
27.
x7c2
d2
18p
44p 9p3
cd
cdx2
x5
p2� q2
©G
lenc
oe/M
cGra
w-H
ill45
8G
lenc
oe A
lgeb
ra 1
Det
erm
ine
wh
eth
er e
ach
exp
ress
ion
is
a m
onom
ial.
Wri
te y
esor
no.
Exp
lain
.
1.N
o;
this
invo
lves
th
e q
uo
tien
t,n
ot
the
pro
du
ct,o
f va
riab
les.
2.Ye
s;th
is is
th
e p
rod
uct
of
a n
um
ber
,,a
nd
tw
o v
aria
ble
s.
Sim
pli
fy.
3.(�
5x2 y
)(3x
4 )�
15x
6 y4.
(2ab
2 c2 )
(4a3
b2c2
)8a
4 b4 c
4
5.(3
cd4 )
(�2c
2 )�
6c3 d
46.
(4g3
h)(
�2g
5 )�
8g8 h
7.(�
15xy
4 )��
xy3 �
5x2 y
78.
(�xy
)3(x
z)�
x4 y
3 z
9.(�
18m
2 n)2��
mn
2 ��
54m
5 n4
10.(
0.2a
2 b3 )
20.
04a4
b6
11. �
p �2p
212
. �cd
3 �2c2
d6
13.(
0.4k
3 )3
0.06
4k9
14.[
(42 )
2 ]2
48o
r 65
,536
GEO
MET
RYE
xpre
ss t
he
area
of
each
fig
ure
as
a m
onom
ial.
15.
16.
17.
18a
3 b6
(25x
6 )�
12a3
c4
GEO
MET
RYE
xpre
ss t
he
volu
me
of e
ach
sol
id a
s a
mon
omia
l.
18.
19.
20.
27h
6m
4 n5
(63g
4 )�
21.C
OU
NTI
NG
A p
anel
of
fou
r li
ght
swit
ches
can
be
set
in 2
4w
ays.
A p
anel
of
five
lig
ht
swit
ches
can
set
in
tw
ice
this
man
y w
ays.
In h
ow m
any
way
s ca
n f
ive
ligh
t sw
itch
es
be s
et?
25o
r 32
22.H
OB
BIE
ST
awa
wan
ts t
o in
crea
se h
er r
ock
coll
ecti
on b
y a
pow
er o
f th
ree
this
yea
r an
dth
en i
ncr
ease
it
agai
n b
y a
pow
er o
f tw
o n
ext
year
.If
she
has
2 r
ocks
now
,how
man
yro
cks
wil
l sh
e h
ave
afte
r th
e se
con
d ye
ar?
26o
r 64
7g2
3g
m3 n
mn3
n
3h2
3h2
3h2
6ac3
4a2 c
5x3
6a2 b
4
3ab2
1 � 161 � 4
4 � 92 � 3
1 � 6
1 � 3
1 � 2b3 c
2�
2
21a2
�7b
Pra
ctic
e (
Ave
rag
e)
Mu
ltip
lyin
g M
on
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-1
8-1
Answers (Lesson 8-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csM
ult
iply
ing
Mo
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-1
8-1
©G
lenc
oe/M
cGra
w-H
ill45
9G
lenc
oe A
lgeb
ra 1
Lesson 8-1
Pre-
Act
ivit
yW
hy
doe
s d
oub
lin
g sp
eed
qu
adru
ple
bra
kin
g d
ista
nce
?
Rea
d th
e in
trod
uct
ion
to
Les
son
8-1
at
the
top
of p
age
410
in y
our
text
book
.
Fin
d tw
o ex
ampl
es i
n t
he
tabl
e to
ver
ify
the
stat
emen
t th
at w
hen
spe
ed i
sdo
ubl
ed,t
he
brak
ing
dist
ance
is
quad
rupl
ed.W
rite
you
r ex
ampl
es i
n t
he
tabl
e.
Sp
eed
Bra
kin
g D
ista
nce
S
pee
d D
ou
ble
d
Bra
kin
g D
ista
nce
(m
iles
per
ho
ur)
(fee
t)(m
iles
per
ho
ur)
Qu
adru
ple
d (
feet
)
2020
4080
3045
6018
0
Rea
din
g t
he
Less
on
1.D
escr
ibe
the
expr
essi
on 3
xyu
sin
g th
e te
rms
mon
omia
l,co
nst
ant,
vari
able
,an
d pr
odu
ct.
Th
e m
on
om
ial 3
xyis
th
e p
rod
uct
of
the
con
stan
t 3
and
th
e va
riab
les
xan
d y
.
2.C
ompl
ete
the
char
t by
ch
oosi
ng
the
prop
erty
th
at c
an b
e u
sed
to s
impl
ify
each
expr
essi
on.T
hen
sim
plif
y th
e ex
pres
sion
.
Exp
ress
ion
Pro
per
tyE
xpre
ssio
n S
imp
lifie
d
Pro
duct
of
Pow
ers
35�
32P
ower
of
a P
ower
37o
r 21
87P
ower
of
a P
rodu
ct
Pro
duct
of
Pow
ers
(a3 )
4P
ower
of
a P
ower
a12
Pow
er o
f a
Pro
duct
Pro
duct
of
Pow
ers
(�4x
y)5
Pow
er o
f a
Pow
er
�10
24x
5 y5
Pow
er o
f a
Pro
duct
Hel
pin
g Y
ou
Rem
emb
er
3.W
rite
an
exa
mpl
e of
eac
h o
f th
e th
ree
prop
erti
es o
f po
wer
s di
scu
ssed
in
th
is l
esso
n.
Th
en,u
sin
g th
e ex
ampl
es,e
xpla
in h
ow t
he
prop
erty
is
use
d to
sim
plif
y th
em.
Sam
ple
an
swer
:F
or
z2�
z5 ,
sin
ce t
he
bas
es a
re t
he
sam
e,u
se t
he
Pro
du
ct o
f P
ow
ers
Pro
per
ty a
nd
ad
d t
he
exp
on
ents
to
get
z7 .
Fo
r (a
4 )3 ,
use
th
e P
ow
er o
f a
Po
wer
Pro
per
ty.M
ult
iply
th
e ex
po
nen
ts t
o g
et a
12.
Fo
r (3
rs)3
,use
th
e P
ow
er o
f a
Pro
du
ct P
rop
erty
.Rai
se t
he
con
stan
t an
dea
ch v
aria
ble
to
th
e p
ow
er t
o g
et 2
7 r3 s
3 .
©G
lenc
oe/M
cGra
w-H
ill46
0G
lenc
oe A
lgeb
ra 1
An
Wan
g
An
Wan
g (1
920–
1990
) w
as a
n A
sian
-Am
eric
an w
ho
beca
me
one
of t
he
pion
eers
of
the
com
pute
r in
dust
ry i
n t
he
Un
ited
Sta
tes.
He
grew
up
inS
han
ghai
,Ch
ina,
but
cam
e to
th
e U
nit
ed S
tate
s to
fu
rth
er h
is s
tudi
esin
sci
ence
.In
194
8,h
e in
ven
ted
a m
agn
etic
pu
lse
con
trol
lin
g de
vice
that
vas
tly
incr
ease
d th
e st
orag
e ca
paci
ty o
f co
mpu
ters
.He
late
rfo
un
ded
his
ow
n c
ompa
ny,
Wan
g L
abor
ator
ies,
and
beca
me
a le
ader
in
the
deve
lopm
ent
of d
eskt
op c
alcu
lato
rs a
nd
wor
d pr
oces
sin
g sy
stem
s.In
198
8,W
ang
was
ele
cted
to
the
Nat
ion
al I
nve
nto
rs H
all
of F
ame.
Dig
ital
com
pute
rs s
tore
in
form
atio
n a
s n
um
bers
.Bec
ause
th
eel
ectr
onic
cir
cuit
s of
a c
ompu
ter
can
exi
st i
n o
nly
on
e of
tw
o st
ates
,op
en o
r cl
osed
,th
e n
um
bers
th
at a
re s
tore
d ca
n c
onsi
st o
f on
ly t
wo
digi
ts,0
or
1.N
um
bers
wri
tten
usi
ng
only
th
ese
two
digi
ts a
re c
alle
db
inar
y n
um
ber
s.T
o fi
nd
the
deci
mal
val
ue
of a
bin
ary
nu
mbe
r,yo
uu
se t
he
digi
ts t
o w
rite
a p
olyn
omia
l in
2.F
or i
nst
ance
,th
is i
s h
ow t
ofi
nd
the
deci
mal
val
ue
of t
he
nu
mbe
r 10
0110
1 2.(
Th
e su
bscr
ipt
2 in
dica
tes
that
th
is i
s a
bin
ary
nu
mbe
r.)
1001
101 2
�1
�2 �
6 ��
0 �
2 �5 �
�0
�2 �
4 ��
1 �
2 �3 �
�1
�2 �
2 ��
0 �
2 �1 �
�1
�2 �
0 ��
1 �
6 �4 �
�0
�3 �2 �
�0
�1 �6 �
�1
�8 �
�1
�4 �
�0
�2 �
�1
�1 �
�64
�0
�0
�8
�4
�0
�1
�77
Fin
d t
he
dec
imal
val
ue
of e
ach
bin
ary
nu
mb
er.
1.11
112
152.
1000
0 216
3.11
0000
112
195
4.10
1110
012
185
Wri
te e
ach
dec
imal
nu
mb
er a
s a
bin
ary
nu
mb
er.
5.8
1000
6.11
1011
7.29
1110
18.
117
1110
101
9.T
he
char
t at
th
e ri
ght
show
s a
set
of d
ecim
al
code
nu
mbe
rs t
hat
is
use
d w
idel
y in
sto
rin
g le
tter
s of
th
e al
phab
et i
n a
com
pute
r's
mem
ory.
Fin
d th
e co
de n
um
bers
for
th
e le
tter
s of
you
r n
ame.
Th
en w
rite
th
e co
de f
or y
our
nam
e u
sin
g bi
nar
y n
um
bers
. An
swer
s w
ill v
ary.
Th
e A
mer
ican
Sta
nd
ard
Gu
ide
for
Info
rmat
ion
Inte
rch
ang
e (A
SC
II)
A65
N78
a97
n11
0B
66O
79b
98o
111
C67
P80
c99
p11
2D
68Q
81d
100
q11
3E
69R
82e
101
r11
4F
70S
83f
102
s11
5G
71T
84g
103
t11
6H
72U
85h
104
u11
7I
73V
86i
105
v11
8J
74W
87j
106
w11
9K
75X
88k
107
x12
0L
76Y
89l
108
y12
1M
77Z
90m
109
z12
2
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-1
8-1
Answers (Lesson 8-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Div
idin
g M
on
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-2
8-2
©G
lenc
oe/M
cGra
w-H
ill46
1G
lenc
oe A
lgeb
ra 1
Lesson 8-2
Qu
oti
ents
of
Mo
no
mia
lsT
o di
vide
tw
o po
wer
s w
ith
th
e sa
me
base
,su
btra
ct t
he
expo
nen
ts.
Qu
oti
ent
of
Po
wer
sF
or a
ll in
tege
rs m
and
nan
d an
y no
nzer
o nu
mbe
r a,
�
am�
n .
Po
wer
of
a Q
uo
tien
tF
or a
ny in
tege
r m
and
any
real
num
bers
aan
d b,
b�
0, �
�m�
.a
m� b
ma � b
am
� an
Sim
pli
fy
.Ass
um
e
nei
ther
an
or b
is e
qu
al t
o ze
ro.
��
���
Gro
up p
ower
s w
ith t
he s
ame
base
.
�(a
4 �
1 )(b
7 �
2 )Q
uotie
nt o
f P
ower
s
�a3
b5S
impl
ify.
Th
e qu
otie
nt
is a
3 b5
.
b7� b2
a4� a
a4 b7
� ab2
a4 b
7� a
b2S
imp
lify
��3 .
Ass
um
e th
at b
is n
ot e
qu
al t
o ze
ro.
��3
�P
ower
of
a Q
uotie
nt
�P
ower
of
a P
rodu
ct
�P
ower
of
a P
ower
�Q
uotie
nt o
f P
ower
s
Th
e qu
otie
nt
is
.8a
9 b9
�27
8a9 b
9�
27
8a9 b
15�27
b6
23 (a3 )
3 (b5 )
3�
�(3
)3 (b2 )
3
(2a3 b
5 )3
�(3
b2 )3
2a3 b
5�
3b2
2a3 b
5�
3b2
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sim
pli
fy.A
ssu
me
that
no
den
omin
ator
is
equ
al t
o ze
ro.
1.53
or
125
2.m
23.
p3 n
3
4.a
5.y
6.�
y2
7.y
28.
��3
8a3 b
39.
��3
p6 q
6
10. �
�416
v4
11. �
�4r4
s812
.r4
s4
r7 s7 t
2� s3 r
3 t2
81 � 163r
6 s3
� 2r5 s
2v5 w
3� v4 w
3
64 � 274p
4 q4
� 3p2 q
22a
2 b�
axy
6� y4 x
1 � 7�
2y7
� 14y5
x5 y3
� x5 y2
a2� a
p5 n4
� p2 nm
6� m
455� 52
©G
lenc
oe/M
cGra
w-H
ill46
2G
lenc
oe A
lgeb
ra 1
Neg
ativ
e Ex
po
nen
tsA
ny
non
zero
nu
mbe
r ra
ised
to
the
zero
pow
er i
s 1;
for
exam
ple,
(�0.
5)0
�1.
An
y n
onze
ro n
um
ber
rais
ed t
o a
neg
ativ
e po
wer
is
equ
al t
o th
e re
cipr
ocal
of
the
nu
mbe
r ra
ised
to
the
oppo
site
pow
er;f
or e
xam
ple,
6�3
�.T
hes
e de
fin
itio
ns
can
be
use
d to
sim
plif
y ex
pres
sion
s th
at h
ave
neg
ativ
e ex
pon
ents
.
Zer
o E
xpo
nen
tF
or a
ny n
onze
ro n
umbe
r a,
a0
�1.
Neg
ativ
e E
xpo
nen
t P
rop
erty
For
any
non
zero
num
ber
aan
d an
y in
tege
r n,
a�
n�
and
�an
.
Th
e si
mpl
ifie
d fo
rm o
f an
exp
ress
ion
con
tain
ing
neg
ativ
e ex
pon
ents
mu
st c
onta
in o
nly
posi
tive
exp
onen
ts.
Sim
pli
fy
.Ass
um
e th
at t
he
den
omin
ator
is
not
eq
ual
to
zero
.
��
����
���
Gro
up p
ower
s w
ith t
he s
ame
base
.
�(a
�3
�2 )
(b6
�6 )
(c5 )
Quo
tient
of
Pow
ers
and
Neg
ativ
e E
xpon
ent
Pro
pert
ies
�a�
5 b0 c
5S
impl
ify.
��
�(1)c
5N
egat
ive
Exp
onen
t an
d Z
ero
Exp
onen
t P
rope
rtie
s
�S
impl
ify.
Th
e so
luti
on i
s .
Sim
pli
fy.A
ssu
me
that
no
den
omin
ator
is
equ
al t
o ze
ro.
1.25
or
322.
m5
3.
4.b
5.6.
a6b
8
7.x
68.
9.
10.
11. �
�01
12.
�m
3� 32
n10
(�2m
n2 )
�3
��
4m�
6 n4
4m2 n
2� 8m
�1 �
1� st
2s�
3 t�
5� (s
2 t3 )
�1
9s3
� u11
(3st
)2 u�
4�
�s�
1 t2 u
736
� a2 b6
(6a�
1 b)2
��
(b2 )
4x4
y0� x�
2
(a2 b
3 )2
� (ab)
�2
w � 4y2
(�x�
1y)
0�
�4w
�1 y
2b�
4� b�
5
1� p
11p�
8� p3
m� m
�4
22� 2�
3
c5� 4a
5
c5� 4a
51 � a51 � 41 � 41 � 4
1� c�
5b6� b6
a�3
� a24 � 16
4a�
3 b6
��
16a2 b
6 c�
5
4a�
3 b6
��
16a
2 b6 c
�5
1� a�
n1 � an
1 � 63
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Div
idin
g M
on
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-2
8-2
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 8-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
ract
ice
Div
idin
g M
on
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-2
8-2
©G
lenc
oe/M
cGra
w-H
ill46
3G
lenc
oe A
lgeb
ra 1
Lesson 8-2
Sim
pli
fy.A
ssu
me
that
no
den
omin
ator
is
equ
al t
o ze
ro.
1.61
or
62.
94o
r 65
61
3.x
24.
5.6.
3d
7.8.
u2
9.a2
b3
10.
m4
11.
�12
.�
4x2 y
z3
13. �
�214
.4�
4
15.8
�2
16. �
��2
17. �
��1
18.
h9
19.k
0 (k4
)(k�
6 )20
.k�
1 (��
6 )(m
3 )
21.
22. �
�01
23.
24.
3x5 y
2
25.
�26
.�
8x5 y
2�
z48
x6 y7 z
5�
��
6xy5 z
63 � u
4�
15w
0 u�
1�
�5u
3
15x6 y
�9
� 5xy�
11g
4 h2
�f5
f�5 g
4� h
�2
16p5 q
2� 2p
3 q3
1 � f11f�
7� f4
m3
� k�6
1 � k2
h3
� h�
611 � 9
9 � 11
9 � 255 � 3
1 � 64
1� 25
616
p14
� 49s4
4p7
� 7s2
32x3 y
2 z5
��
�8x
yz2
3w � u3
�21
w5 u
2�
�7w
4 u5
m7 n
2� m
3 n2
a3 b5
� ab2
w4 u
3� w
4 un
4� 3
12n
5� 36
n
9d7
� 3d6
1 � m2
m � m3
1 � s2r3 s
2� r3 s
4x4� x2
912� 98
65� 64
©G
lenc
oe/M
cGra
w-H
ill46
4G
lenc
oe A
lgeb
ra 1
Sim
pli
fy.A
ssu
me
that
no
den
omin
ator
is
equ
al t
o ze
ro.
1.84
or
4096
2.a3
b3
3.y
4.m
n5.
�6.
2yz
7.�
�38.
��2
9.�
10.x
3 (y�
5 )(x
�8 )
11.p
(q�
2 )(r
�3 )
12.1
2�2
13. �
��2
14. �
��4
15.
2rs5
16.
�17
.2c
4 f7
18. �
�01
19.
20.
�21
.
22.
23.
24.
25. �
��5
26. �
��1
27. �
��2
28.B
IOLO
GY
A l
ab t
ech
nic
ian
dra
ws
a sa
mpl
e of
blo
od.A
cu
bic
mil
lim
eter
of
the
bloo
dco
nta
ins
223
wh
ite
bloo
d ce
lls
and
225
red
bloo
d ce
lls.
Wh
at i
s th
e ra
tio
of w
hit
e bl
ood
cell
s to
red
blo
od c
ells
?
29. C
OU
NTI
NG
Th
e n
um
ber
of t
hre
e-le
tter
“w
ords
”th
at c
an b
e fo
rmed
wit
h t
he
En
glis
hal
phab
et i
s 26
3 .T
he
nu
mbe
r of
fiv
e-le
tter
“w
ords
”th
at c
an b
e fo
rmed
is
265 .
How
man
yti
mes
mor
e fi
ve-l
ette
r “w
ords
”ca
n b
e fo
rmed
th
an t
hre
e-le
tter
“w
ords
”?67
6
1� 48
4
9x2
� 4y2 z
62x
3 y2 z
� 3x4yz
�2
c8� 7d
2 e4
7c�
3 d3
� c5 de�
4q
10� r25
q�1 r
3� qr
�2
a4� 40
b7
(2a�
2 b)�
3�
�5a
2 b4
j� k15
(j�
1 k3 )
�4
�j3 k
3m
2� n
2m
�2 n
�5
��
(m4 n
3 )�
1
r � 27r4
� (3r)
36t
2 u4
�v9
�12
t�1 u
5 v�
4�
�2t
�3 u
v5g
8 h2
�9
6f�
2 g3 h
5�
�54
f�2 g
�5 h
3
x�3 y
5�4�
38c
3 d2 f
4�
�4c
�1 d
2 f�
33 � u4
�15
w0 u
�1
��
5u3
22r3 s
2� 11
r2 s�
381 � 25
64 � 3
49 � 93 � 7
1� 14
4p
� q2 r
31
� x5 y5
1� 6c
3�
4c2
� 24c5
36w
10� 49
p12
s66w
5� 7p
6 s3
64f9 g
3� 27
h18
4f3 g
� 3h6
8y7 z
6� 4y
6 z5
5d2
�4
5c2 d
3� �
4c2 d
m5 n
p� m
4 p
xy2
� xya4 b
6� ab
388� 84
Pra
ctic
e (
Ave
rag
e)
Div
idin
g M
on
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-2
8-2
Answers (Lesson 8-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csD
ivid
ing
Mo
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-2
8-2
©G
lenc
oe/M
cGra
w-H
ill46
5G
lenc
oe A
lgeb
ra 1
Lesson 8-2
Pre-
Act
ivit
yH
ow c
an y
ou c
omp
are
pH
lev
els?
Rea
d th
e in
trod
uct
ion
to
Les
son
8-2
at
the
top
of p
age
417
in y
our
text
book
.
•In
th
e fo
rmu
la c
��
�pH,i
den
tify
th
e ba
se a
nd
the
expo
nen
t.
bas
e �
,exp
on
ent
�p
H
•H
ow d
o yo
u t
hin
k c
wil
l ch
ange
as
the
expo
nen
t in
crea
ses?
cw
ill d
ecre
ase.
Rea
din
g t
he
Less
on
1.E
xpla
in w
hat
th
e st
atem
ent
�am
�n
mea
ns.
To d
ivid
e tw
o p
ow
ers
that
hav
e th
e sa
me
bas
e,su
btr
act
the
exp
on
ents
.
2.To
fin
d c
in t
he f
orm
ula
c�
��pH
,you
can
fin
d th
e po
wer
of
the
num
erat
or,t
he p
ower
of
the
den
omin
ator
,an
d di
vide
.Th
is i
s an
exa
mpl
e of
wh
at p
rope
rty?
Po
wer
of
a Q
uo
tien
t P
rop
erty
3.U
se t
he
Qu
otie
nt
of P
ower
s P
rope
rty
to e
xpla
in w
hy
30�
1.S
amp
le a
nsw
er:
�1.
Th
e Q
uo
tien
t o
f P
ow
ers
Pro
per
ty s
ays
that
wh
en y
ou
div
ide
two
po
wer
s th
at h
ave
the
sam
e b
ase,
you
su
btr
act
the
exp
on
ents
.
So
�
30.
4.C
onsi
der
the
expr
essi
on 4
�3 .
a.E
xpla
in w
hy
the
expr
essi
on 4
�3
is n
ot s
impl
ifie
d.A
n e
xpre
ssio
n in
volv
ing
exp
on
ents
is n
ot
con
sid
ered
sim
plif
ied
if t
he
exp
ress
ion
co
nta
ins
neg
ativ
e ex
po
nen
ts.
b.
Def
ine
the
term
rec
ipro
cal.
Th
e re
cip
roca
l of
a n
um
ber
is 1
div
ided
by
the
nu
mb
er.
c.4�
3is
th
e re
cipr
ocal
of
wh
at p
ower
of
4?43
d.
Wh
at i
s th
e si
mpl
ifie
d fo
rm o
f 4�
3 ?o
r
Hel
pin
g Y
ou
Rem
emb
er
5.D
escr
ibe
how
you
wou
ld h
elp
a fr
ien
d w
ho
nee
ds t
o si
mpl
ify
the
expr
essi
on
.
Div
ide
the
con
stan
ts a
nd
gro
up
po
wer
s w
ith
th
e sa
me
bas
e to
get
���
�.Use
th
e Q
uo
tien
t o
f P
ow
ers
Pro
per
ty t
o g
et (
2)(x
2�5 )
or
(2)(
x�3).
To s
imp
lify
(2)(
x�3 )
,use
th
e N
egat
ive
Exp
on
ent
Pro
per
ty t
o g
et
(2) �
�,or
.2 � x3
1 � x3x2� x5
4 � 2
4x2
� 2x5
1 � 641 � 43
34� 34
34� 34
1 � 10am� an
1 � 10
1 � 10
©G
lenc
oe/M
cGra
w-H
ill46
6G
lenc
oe A
lgeb
ra 1
Pat
tern
s w
ith
Pow
ers
Use
you
r ca
lcu
lato
r,if
nec
essa
ry,t
o co
mpl
ete
each
pat
tern
.
a.21
0�
b.
510
�c.
410
�
29�
59�
49�
28�
58�
48�
27�
57�
47�
26�
56�
46�
25�
55�
45�
24�
54�
44�
23�
53�
43�
22�
52�
42�
21�
51�
41�
Stu
dy
the
pat
tern
s fo
r a,
b,a
nd
c a
bov
e.T
hen
an
swer
th
e q
ues
tion
s.
1.D
escr
ibe
the
patt
ern
of
the
expo
nen
ts f
rom
th
e to
p of
eac
h c
olu
mn
to
the
bott
om.
Th
e ex
po
nen
ts d
ecre
ase
by o
ne
fro
m e
ach
ro
w t
o t
he
on
e b
elo
w.
2.D
escr
ibe
the
patt
ern
of
the
pow
ers
from
th
e to
p of
th
e co
lum
n t
o th
e bo
ttom
.To
get
each
po
wer
,div
ide
the
po
wer
on
th
e ro
w a
bov
e by
th
e b
ase
(2,5
,or
4).
3.W
hat
wou
ld y
ou e
xpec
t th
e fo
llow
ing
pow
ers
to b
e?20
150
140
1
4.R
efer
to
Exe
rcis
e 3.
Wri
te a
ru
le.T
est
it o
n p
atte
rns
that
you
obt
ain
usi
ng
22,2
5,an
d 24
as b
ases
.A
ny n
on
zero
nu
mb
er t
o t
he
zero
po
wer
eq
ual
s o
ne.
Stu
dy
the
pat
tern
bel
ow.T
hen
an
swer
th
e q
ues
tion
s.
03�
002
�0
01�
000
�0�
1do
es n
ot e
xist
.0�
2do
es n
ot e
xist
.0�
3do
es n
ot e
xist
.
5.W
hy
do 0
�1 ,
0�2 ,
and
0�3
not
exi
st?
Neg
ativ
e ex
po
nen
ts a
re n
ot
def
ined
un
less
th
e b
ase
is n
on
zero
.
6.B
ased
upo
n t
he
patt
ern
,can
you
det
erm
ine
wh
eth
er 0
0ex
ists
? N
o,s
ince
th
e p
atte
rn 0
n�
0 b
reak
s d
ow
n f
or
n�
1.
7.T
he
sym
bol
00is
cal
led
an i
nd
eter
min
ate,
wh
ich
mea
ns
that
it
has
no
un
iqu
e va
lue.
Thu
s it
doe
s no
t ex
ist
as a
uni
que
real
num
ber.
Why
do
you
thin
k th
at 0
0ca
nnot
equ
al 1
?
An
swer
s w
ill v
ary.
On
e an
swer
is t
hat
if 0
0�
1,th
en 1
��
��
�0 ,
wh
ich
is a
fal
se r
esu
lt,s
ince
div
isio
n b
y ze
ro is
no
t al
low
ed.T
hu
s,00
can
no
t eq
ual
1.
1 � 010� 00
1 � 1
?
45
216
254
6412
58
256
625
1610
2431
2532
4096
15,6
2564
16,3
8478
,125
128
65,5
3639
0,62
525
626
2,14
41,
953,
125
512
1,04
8,57
69,
765,
625
1024
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-2
8-2
Answers (Lesson 8-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Sci
enti
fic
No
tati
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-3
8-3
©G
lenc
oe/M
cGra
w-H
ill46
7G
lenc
oe A
lgeb
ra 1
Lesson 8-3
Scie
nti
fic
No
tati
on
Kee
pin
g tr
ack
of p
lace
val
ue
in v
ery
larg
e or
ver
y sm
all
nu
mbe
rsw
ritt
en i
n s
tan
dard
for
m m
ay b
e di
ffic
ult
.It
is m
ore
effi
cien
t to
wri
te s
uch
nu
mbe
rs i
nsc
ien
tifi
c n
otat
ion
.A n
um
ber
is e
xpre
ssed
in
sci
enti
fic
not
atio
n w
hen
it
is w
ritt
en a
s a
prod
uct
of
two
fact
ors,
one
fact
or t
hat
is
grea
ter
than
or
equ
al t
o 1
and
less
th
an 1
0 an
d on
efa
ctor
th
at i
s a
pow
er o
f te
n.
Sci
enti
fic
No
tati
on
Anu
mbe
r is
in s
cien
tific
not
atio
n w
hen
it is
in t
he f
orm
a�
10n ,
whe
re 1
a
10
an
d n
is a
n in
tege
r.
Exp
ress
3.5
2 �
104
inst
and
ard
not
atio
n.
3.52
�10
4�
3.52
�10
,000
�35
,200
Th
e de
cim
al p
oin
t m
oved
4 p
lace
s to
th
eri
ght.
Exp
ress
37,
600,
000
insc
ien
tifi
c n
otat
ion
.
37,6
00,0
00 �
3.76
�10
7
Th
e de
cim
al p
oin
t m
oved
7 p
lace
s so
th
at i
tis
bet
wee
n t
he
3 an
d th
e 7.
Sin
ce
37,6
00,0
00 �
1,th
e ex
pon
ent
is p
osit
ive.
Exp
ress
6.2
1 �
10�
5in
stan
dar
d n
otat
ion
.
6.21
�10
�5
�6.
21 �
�6.
21 �
0.00
001
�0.
0000
621
The
dec
imal
poi
nt m
oved
5 p
lace
s to
the
lef
t.
Exp
ress
0.0
0005
49 i
nsc
ien
tifi
c n
otat
ion
.
0.00
0054
9 �
5.49
�10
�5
Th
e de
cim
al p
oin
t m
oved
5 p
lace
s so
th
at i
tis
bet
wee
n t
he
5 an
d th
e 4.
Sin
ce
0.00
0054
9
1,th
e ex
pon
ent
is n
egat
ive.
1� 10
5
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exam
ple
3Ex
ampl
e 3
Exam
ple
4Ex
ampl
e 4
Exer
cises
Exer
cises
Exp
ress
eac
h n
um
ber
in
sta
nd
ard
not
atio
n.
1.3.
65 �
105
2.7.
02 �
10�
43.
8.00
3 �
108
365,
000
0.00
0702
800,
300,
000
4.7.
451
�10
65.
5.91
�10
06.
7.99
�10
�1
7,45
1,00
05.
910.
799
7.8.
9354
�10
108.
8.1
�10
�9
9.4
�10
15
89,3
54,0
00,0
000.
0000
0000
814,
000,
000,
000,
000,
000
Exp
ress
eac
h n
um
ber
in
sci
enti
fic
not
atio
n.
10.0
.000
0456
11.0
.000
0112
.590
,000
,000
4.56
�10
�5
1 �
10�
55.
9 �
108
13.0
.000
0000
0012
14.0
.000
0804
3615
.0.0
3621
1.2
�10
�10
8.04
36 �
10�
53.
621
�10
�2
16.4
33 �
104
17.0
.004
2 �
10�
318
.50,
000,
000,
000
4.33
�10
64.
2 �
10�
65
�10
10
©G
lenc
oe/M
cGra
w-H
ill46
8G
lenc
oe A
lgeb
ra 1
Pro
du
cts
and
Qu
oti
ents
wit
h S
cien
tifi
c N
ota
tio
nYo
u c
an u
se p
rope
rtie
s of
pow
ers
to c
ompu
te w
ith
nu
mbe
rs w
ritt
en i
n s
cien
tifi
c n
otat
ion
.
Eva
luat
e (6
.7 �
103 )
(2 �
10�
5 ).E
xpre
ss t
he
resu
lt i
n s
cien
tifi
c an
dst
and
ard
not
atio
n.
(6.7
�10
3 )(2
�10
�5 )
�(6
.7 �
2)(1
03�
10�
5 )A
ssoc
iativ
e P
rope
rty
�13
.4 �
10�
2P
rodu
ct o
f P
ower
s
�(1
.34
�10
1 ) �
10�
213
.4 �
1.34
�10
1
�1.
34 �
(101
�10
�2 )
Ass
ocia
tive
Pro
pert
y
�1.
34 �
10�
1or
0.1
34P
rodu
ct o
f P
ower
s
Th
e so
luti
on i
s 1.
34 �
10�
1or
0.1
34.
Eva
luat
e .E
xpre
ss t
he
resu
lt i
n s
cien
tifi
c an
d
stan
dar
d n
otat
ion
.
��
���
Ass
ocia
tive
Pro
pert
y
�0.
368
�10
3Q
uotie
nt o
f P
ower
s
�(3
.68
�10
�1 )
�10
30.
368
�3.
68 �
10�
1
�3.
68 �
(10�
1�
103 )
Ass
ocia
tive
Pro
pert
y
�3.
68 �
102
or 3
68P
rodu
ct o
f P
ower
s
Th
e so
luti
on i
s 3.
68 �
102
or 3
68.
Eva
luat
e.E
xpre
ss e
ach
res
ult
in
sci
enti
fic
and
sta
nd
ard
not
atio
n.
1.2.
3.(3
.2 �
10�
2 )(2
.0 �
102 )
7 �
10;
701.
5 �
103 ;
1500
6.4
�10
0 ;6.
4
4.5.
(7.7
�10
5 )(2
.1 �
102 )
6.
5.28
�10
3 ;52
801.
617
�10
8 ;16
1,70
0,00
01.
35 �
10�
2 ;0.
0135
7.(3
.3 �
105 )
(1.5
�10
�4 )
8.9.
4.95
�10
1 ;49
.53
�10
2 ;30
01.
6 �
10�
6 ;0.
0000
016
10.F
UEL
CO
NSU
MPT
ION
Nor
th A
mer
ica
burn
ed 4
.5 �
1016
BT
U o
f pe
trol
eum
in
199
8.A
t th
is r
ate,
how
man
y B
TU
’s w
ill
be b
urn
ed i
n 9
yea
rs?
Sour
ce: T
he N
ew Y
ork
Times
200
1 Al
man
ac
4.05
�10
17
11.O
IL P
RO
DU
CTI
ON
If t
he
Un
ited
Sta
tes
prod
uce
d 6.
25 �
109
barr
els
of c
rude
oil
in
1998
,an
d C
anad
a pr
odu
ced
1.98
�10
9ba
rrel
s,w
hat
is
the
quot
ien
t of
th
eir
prod
uct
ion
rate
s? W
rite
a s
tate
men
t u
sin
g th
is q
uot
ien
t.So
urce
: The
New
Yor
k Tim
es 2
001
Alm
anac
Ab
ou
t 3.
16;
Sam
ple
an
swer
:Th
e U
nit
ed S
tate
s p
rod
uce
s m
ore
th
an
3 ti
mes
th
e cr
ud
e o
il o
f C
anad
a.
4 �
10�
4�
�2.
5 �
102
3.3
�10
�12
��
1.1
�10
�14
9.72
�10
8�
�7.
2 �
1010
1.26
72 �
10�
8�
�2.
4 �
10�
12
3 �
10�
12�
�2
�10
�15
1.4
�10
4�
�2
�10
2
108
� 105
1.50
88�
4.1
1.50
88 �
108
��
4.1
�10
5
1.50
88 �
108
��
4.1
�10
5
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Sci
enti
fic
No
tati
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-3
8-3
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Answers (Lesson 8-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Sci
enti
fic
No
tati
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-3
8-3
©G
lenc
oe/M
cGra
w-H
ill46
9G
lenc
oe A
lgeb
ra 1
Lesson 8-3
Exp
ress
eac
h n
um
ber
in
sta
nd
ard
not
atio
n.
1.4
�10
32.
2 �
108
3.3.
2 �
105
4000
200,
000,
000
320,
000
4.3
�10
�6
5.9
�10
�2
6.4.
7 �
10�
7
0.00
0003
0.09
0.00
0000
47
AST
RO
NO
MY
Exp
ress
th
e n
um
ber
in
eac
h s
tate
men
t in
sta
nd
ard
not
atio
n.
7.T
he
diam
eter
of
Jupi
ter
is 1
.429
84 �
105
kilo
met
ers.
142,
984
8.T
he
surf
ace
den
sity
of
the
mai
n r
ing
arou
nd
Jupi
ter
is 5
�10
�6
gram
s pe
r ce
nti
met
ersq
uar
ed.
0.00
0005
9.T
he
min
imu
m d
ista
nce
fro
m M
ars
to E
arth
is
5.45
�10
7ki
lom
eter
s.54
,500
,000
Exp
ress
eac
h n
um
ber
in
sci
enti
fic
not
atio
n.
10.4
1,00
0,00
011
.65,
100
12.2
83,0
00,0
00
4.1
�10
76.
51 �
104
2.83
�10
8
13.2
64,7
0114
.0.0
1915
.0.0
0000
7
2.64
701
�10
51.
9 �
10�
27
�10
�6
16.0
.000
0100
3517
.264
.918
.150
�10
2
1.00
35 �
10�
52.
649
�10
21.
5 �
104
Eva
luat
e.E
xpre
ss e
ach
res
ult
in
sci
enti
fic
and
sta
nd
ard
not
atio
n.
19.(
3.1
�10
7 )(2
�10
�5 )
20.(
5 �
10�
2 )(1
.4 �
10�
4 )
6.2
�10
2 ;62
07.
0 �
10�
6 ;0.
0000
07
21.(
3 �
103 )
(4.2
�10
�1 )
22.(
3 �
10�
2 )(5
.2 �
109 )
1.26
�10
3 ;12
601.
56 �
108 ;
156,
000,
000
23.(
2.4
�10
2 )(4
�10
�10
)24
.(1.
5 �
10�
4 )(7
�10
�5 )
9.6
�10
�8 ;
0.00
0000
096
1.05
�10
�8 ;
0.00
0000
0105
25.
26.
3.4
�10
4 ;34
,000
1.8
�10
�2 ;
0.01
8
7.2
�10
�5
��
4 �
10�
35.
1 �
106
��
1.5
�10
2
©G
lenc
oe/M
cGra
w-H
ill47
0G
lenc
oe A
lgeb
ra 1
Exp
ress
eac
h n
um
ber
in
sta
nd
ard
not
atio
n.
1.7.
3 �
107
2.2.
9 �
103
3.9.
821
�10
12
73,0
00,0
0029
009,
821,
000,
000,
000
4.3.
54 �
10�
15.
7.36
42 �
104
6.4.
268
�10
�6
0.35
473
,642
0.00
0004
268
PHY
SIC
SE
xpre
ss t
he
nu
mb
er i
n e
ach
sta
tem
ent
in s
tan
dar
d n
otat
ion
.
7.A
n el
ectr
on h
as a
neg
ativ
e ch
arge
of
1.6
�10
�19
Cou
lom
b.0.
0000
0000
0000
0000
0016
8.In
th
e m
iddl
e la
yer
of t
he
sun
’s a
tmos
pher
e,ca
lled
th
e ch
rom
osph
ere,
the
tem
pera
ture
aver
ages
2.7
8 �
104
degr
ees
Cel
siu
s.27
,800
Exp
ress
eac
h n
um
ber
in
sci
enti
fic
not
atio
n.
9.91
5,60
0,00
0,00
010
.638
711
.845
,320
12.0
.000
0000
0814
9.15
6 �
1011
6.38
7 �
103
8.45
32 �
105
8.14
�10
�9
13.0
.000
0962
114
.0.0
0315
715
.30,
620
16.0
.000
0000
0001
129.
621
�10
�5
3.15
7 �
10�
33.
062
�10
41.
12 �
10�
11
17.5
6 �
107
18.4
740
�10
519
.0.0
76 �
10�
320
.0.0
057
�10
3
5.6
�10
84.
74 �
108
7.6
�10
�5
5.7
or
5.7
�10
0
Eva
luat
e.E
xpre
ss e
ach
res
ult
in
sci
enti
fic
and
sta
nd
ard
not
atio
n.
21.(
5 �
10�
2 )(2
.3 �
1012
)22
.(2.
5 �
10�
3 )(6
�10
15)
1.15
�10
11;
115,
000,
000,
000
1.5
�10
13;
15,0
00,0
00,0
00,0
00
23.(
3.9
�10
3 )(4
.2 �
10�
11)
24.(
4.6
�10
�4 )
(3.1
�10
�1 )
1.63
8 �
10�
7 ;0.
0000
0016
381.
426
�10
�4 ;
0.00
0142
6
25.
26.
27.
2.0
�10
6 ;2,
000,
000
1.6
�10
�5 ;
0.00
0016
2.34
�10
2 ;23
4
28.
29.
30.
2.0
�10
�3 ;
0.00
22.
0 �
107 ;
20,0
00,0
006.
5 �
10�
6 ;0.
0000
065
31.B
IOLO
GY
A c
ubi
c m
illi
met
er o
f h
um
an b
lood
con
tain
s ab
out
5 �
106
red
bloo
d ce
lls.
An
adul
t hu
man
bod
y m
ay c
onta
in a
bout
5 �
106
cubi
c m
illi
met
ers
of b
lood
.Abo
ut h
ow m
any
red
bloo
d ce
lls
does
su
ch a
hu
man
bod
y co
nta
in?
abo
ut
2.5
�10
13o
r 25
tri
llio
n
32.P
OPU
LATI
ON
Th
e po
pula
tion
of A
rizo
na
is a
bou
t 4.
778
�10
6pe
ople
.Th
e la
nd
area
is
abou
t 1.
14 �
105
squ
are
mil
es.W
hat
is
the
popu
lati
on d
ensi
ty p
er s
quar
e m
ile?
abo
ut
42 p
eop
le p
er s
qu
are
mile
2.01
5 �
10�
3�
�3.
1 �
102
1.68
�10
4�
�8.
4 �
10�
41.
82 �
105
��
9.1
�10
7
1.17
�10
2�
�5
�10
�1
6.72
�10
3�
�4.
2 �
108
3.12
�10
3�
�1.
56 �
10�
3
Pra
ctic
e (
Ave
rag
e)
Sci
enti
fic
No
tati
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-3
8-3
Answers (Lesson 8-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
cien
tifi
c N
ota
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-3
8-3
©G
lenc
oe/M
cGra
w-H
ill47
1G
lenc
oe A
lgeb
ra 1
Lesson 8-3
Pre-
Act
ivit
yW
hy
is s
cien
tifi
c n
otat
ion
im
por
tan
t in
ast
ron
omy?
Rea
d th
e in
trod
uct
ion
to
Les
son
8-3
at
the
top
of p
age
425
in y
our
text
book
.
In t
he
tabl
e,ea
ch m
ass
is w
ritt
en a
s th
e pr
odu
ct o
f a
nu
mbe
r an
d a
pow
erof
10.
Loo
k at
th
e fi
rst
fact
or i
n e
ach
pro
duct
.How
are
th
ese
fact
ors
alik
e?
Th
ey a
re a
ll g
reat
er t
han
1 a
nd
less
th
an 1
0.
Rea
din
g t
he
Less
on
1.Is
th
e n
um
ber
0.05
43 �
104
in s
cien
tifi
c n
otat
ion
? E
xpla
in.
No
;th
e fi
rst
fact
or
is le
ss t
han
1.
2.C
ompl
ete
each
sen
ten
ce t
o ch
ange
fro
m s
cien
tifi
c n
otat
ion
to
stan
dard
not
atio
n.
a.T
o ex
pres
s 3.
64 �
106
in s
tan
dard
not
atio
n,m
ove
the
deci
mal
poi
nt
plac
es t
o th
e .
b.
To
expr
ess
7.82
5 �
10�
3in
sta
nda
rd n
otat
ion
,mov
e th
e de
cim
al p
oin
t
plac
es t
o th
e .
3.C
ompl
ete
each
sen
ten
ce t
o ch
ange
fro
m s
tan
dard
not
atio
n t
o sc
ien
tifi
c n
otat
ion
.
a.T
o ex
pres
s 0.
0007
865
in s
cien
tifi
c n
otat
ion
,mov
e th
e de
cim
al p
oin
t pl
aces
to t
he
righ
t an
d w
rite
.
b.
To
expr
ess
54,0
00,0
00,0
00 i
n s
cien
tifi
c n
otat
ion
,mov
e th
e de
cim
al p
oin
t
plac
es t
o th
e le
ft a
nd
wri
te
.
4.W
rite
pos
itiv
eor
neg
ativ
eto
com
plet
e ea
ch s
ente
nce
.
a.po
wer
s of
10
are
use
d to
exp
ress
ver
y la
rge
nu
mbe
rs i
n
scie
nti
fic
not
atio
n.
b.
pow
ers
of 1
0 ar
e u
sed
to e
xpre
ss v
ery
smal
l n
um
bers
in
scie
nti
fic
not
atio
n.
Hel
pin
g Y
ou
Rem
emb
er
5.D
escr
ibe
the
met
hod
you
wou
ld u
se t
o es
tim
ate
how
man
y ti
mes
gre
ater
th
e m
ass
ofS
atu
rn i
s th
an t
he
mas
s of
Plu
to.
Div
ide
5.69
�10
26by
1.2
7 �
1022
.Sin
ce 5
.69
�1.
27 �
4.48
an
d
1026
�10
22is
104
,th
e m
ass
of
Mar
s is
ab
ou
t 4.
48 �
104
tim
es t
he
mas
s o
f P
luto
.
Neg
ativ
e
Po
siti
ve
5.4
�10
10
107.
865
�10
�4
4
left
3
rig
ht
6
©G
lenc
oe/M
cGra
w-H
ill47
2G
lenc
oe A
lgeb
ra 1
Co
nver
tin
g M
etri
c U
nit
sS
cien
tifi
c n
otat
ion
is
con
ven
ien
t to
use
for
un
it c
onve
rsio
ns
in t
he
met
ric
syst
em.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-3
8-3
How
man
y k
ilom
eter
sar
e th
ere
in 4
,300
,000
met
ers?
Div
ide
the
mea
sure
by
the
nu
mbe
r of
met
ers
(100
0) i
n o
ne
kilo
met
er.E
xpre
ssbo
th n
um
bers
in
sci
enti
fic
not
atio
n.
�4.
3 �
103
Th
e an
swer
is
4.3
3 10
3 km
.
4.3
�10
6�
�1
�10
3
Con
vert
370
0 gr
ams
into
mil
ligr
ams.
Mu
ltip
ly b
y th
e n
um
ber
of m
illi
gram
s(1
000)
in
1 g
ram
.
(3.7
�10
3 )(1
�10
3 ) �
3.7
�10
6
Th
ere
are
3.7
�10
6m
g in
370
0 g.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Com
ple
te t
he
foll
owin
g.E
xpre
ss e
ach
an
swer
in
sci
enti
fic
not
atio
n.
1.25
0,00
0 m
�km
2.37
5 km
�m
3.24
7 m
�cm
4.50
00 m
�m
m
5.0.
0004
km
�m
6.0.
01 m
m �
m
7.60
00 m
�m
m8.
340
cm �
km
9.52
,000
mg
�g
10.4
20 k
L �
L
Sol
ve.
11.T
he
plan
et M
ars
has
a d
iam
eter
of
6.76
�10
3km
.Wh
at i
s th
edi
amet
er o
f M
ars
in m
eter
s? E
xpre
ss t
he
answ
er i
n b
oth
sci
enti
fic
and
deci
mal
not
atio
n.
6,76
0,00
0 m
;6.
76 �
106
m
12.T
he
dist
ance
fro
m e
arth
to
the
sun
is
149,
590,
000
km.L
igh
ttr
avel
s 3.
0 �
108
met
ers
per
seco
nd.
How
lon
g do
es i
t ta
ke l
igh
tfr
om t
he
sun
to
reac
h t
he
eart
h i
n m
inu
tes?
Rou
nd
to t
he
nea
rest
hu
ndr
edth
.8.
31 m
in
13.A
lig
ht-
year
is
the
dist
ance
th
at l
igh
t tr
avel
s in
on
e ye
ar.(
See
Exe
rcis
e 12
.) H
ow f
ar i
s a
ligh
t ye
ar i
n k
ilom
eter
s? E
xpre
ss y
our
answ
er i
n s
cien
tifi
c n
otat
ion
.Rou
nd
to t
he
nea
rest
hu
ndr
edth
.9.
46 �
1012
km
4.2
�10
55.
2 �
101
3.4
�10
�3
6 �
106
1 �
10�
54
�10
�1
5 �
106
2.47
�10
4
3.75
�10
52.
5 �
102
Answers (Lesson 8-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Po
lyn
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-4
8-4
©G
lenc
oe/M
cGra
w-H
ill47
3G
lenc
oe A
lgeb
ra 1
Lesson 8-4
Deg
ree
of
a Po
lyn
om
ial
A p
olyn
omia
lis
a m
onom
ial
or a
su
m o
f m
onom
ials
.Ab
inom
ial
is t
he
sum
of
two
mon
omia
ls,a
nd
a tr
inom
ial
is t
he
sum
of
thre
e m
onom
ials
.P
olyn
omia
ls w
ith
mor
e th
an t
hre
e te
rms
hav
e n
o sp
ecia
l n
ame.
Th
e d
egre
eof
a m
onom
ial
is t
he
sum
of
the
expo
nen
ts o
f al
l it
s va
riab
les.
Th
e d
egre
e of
th
e p
olyn
omia
lis
th
e sa
me
as t
he
degr
ee o
f th
e m
onom
ial
term
wit
h t
he
hig
hes
t de
gree
.
Sta
te w
het
her
eac
h e
xpre
ssio
n i
s a
pol
ynom
ial.
If t
he
exp
ress
ion
is
a p
olyn
omia
l,id
enti
fy i
t as
a m
onom
ial,
bin
omia
l,or
tri
nom
ial.
Th
en g
ive
the
deg
ree
of t
he
pol
ynom
ial.
Exp
ress
ion
Po
lyn
om
ial?
Mo
no
mia
l,B
ino
mia
l,D
egre
e o
f th
e o
r Tri
no
mia
l?P
oly
no
mia
l
3x�
7xyz
Yes.
3x
�7x
yz�
3x�
(�7x
yz),
bino
mia
l3
whi
ch is
the
sum
of
two
mon
omia
ls
�25
Yes.
�25
is a
rea
l num
ber.
mon
omia
l0
7n3
�3n
�4
No.
3n�
4�
, w
hich
is n
ot
none
of
thes
e—
a m
onom
ial
Yes.
The
exp
ress
ion
sim
plifi
es t
o9 x
3�
4x�
x�
4 �
2x9x
3�
7x�
4, w
hich
is t
he s
um
trin
omia
l3
of t
hree
mon
omia
ls
Sta
te w
het
her
eac
h e
xpre
ssio
n i
s a
pol
ynom
ial.
If t
he
exp
ress
ion
is
a p
olyn
omia
l,id
enti
fy i
t as
a m
onom
ial,
bin
omia
l,or
tri
nom
ial.
1.36
yes;
mo
no
mia
l2.
�5
no
3.7x
�x
�5
yes;
bin
om
ial
4.8g
2 h�
7gh
�2
yes;
trin
om
ial
5.�
5y�
8n
o6.
6x�
x2ye
s;b
ino
mia
l
Fin
d t
he
deg
ree
of e
ach
pol
ynom
ial.
7.4x
2 y3 z
68.
�2a
bc3
9.15
m1
10.s
�5t
111
.22
012
.18x
2�
4yz
�10
y2
13.x
4�
6x2
�2x
3�
104
14.2
x3y2
�4x
y35
15.�
2r8 s
4�
7r2 s
�4r
7 s6
13
16.9
x2�
yz8
917
.8b
�bc
56
18.4
x4y
�8z
x2�
2x5
5
19.4
x2�
12
20.9
abc
�bc
�d
55
21.h
3 m�
6h4 m
2�
76
1� 4y
2
3 � q2
3 � n4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill47
4G
lenc
oe A
lgeb
ra 1
Wri
te P
oly
no
mia
ls in
Ord
erT
he
term
s of
a p
olyn
omia
l ar
e u
sual
ly a
rran
ged
so t
hat
th
e po
wer
s of
on
e va
riab
le a
re i
n a
scen
din
g(i
ncr
easi
ng)
ord
er o
r d
esce
nd
ing
(dec
reas
ing)
ord
er.
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Po
lyn
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-4
8-4
Arr
ange
th
e te
rms
ofea
ch p
olyn
omia
l so
th
at t
he
pow
ers
ofx
are
in a
scen
din
g or
der
.
a.x4
�x2
5x
3
�x2
�5x
3�
x4
b.
8x3 y
�y2
6x
2 y
xy2
�y2
�xy
2�
6x2 y
�8x
3 y
Arr
ange
th
e te
rms
ofea
ch p
olyn
omia
l so
th
at t
he
pow
ers
ofx
are
in d
esce
nd
ing
ord
er.
a.x4
4x
5�
x2
4x5
�x4
�x2
b.
�6x
y
y3�
x2y2
x4
y2
x4y2
� x
2 y2
�6x
y�
y3
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Arr
ange
th
e te
rms
of e
ach
pol
ynom
ial
so t
hat
th
e p
ower
s of
xar
e in
as
cen
din
g or
der
.
1.5x
�x2
�6
2.6x
�9
�4x
23.
4xy
�2y
�6x
2
6
5x
x2
9
6x�
4x2
2y
4xy
6x
2
4.6y
2 x�
6x2 y
�2
5.x4
�x3
�x2
6.2x
3�
x�
3x7
2
6y2 x
�6x
2 yx
2
x3
x4
�x
2x
3 3x
7
7.�
5cx
�10
c2x3
�15
cx2
8.�
4nx
�5n
3 x3 �
59.
4xy
�2y
�5x
2
�5c
x
15cx
2
10c
2 x3
5 �
4nx
�5n
3 x3
2y
4xy
5x
2
Arr
ange
th
e te
rms
of e
ach
pol
ynom
ial
so t
hat
th
e p
ower
s of
xar
e in
d
esce
nd
ing
ord
er.
10.2
x�
x2�
511
.20x
�10
x2�
5x3
12.x
2�
4yx�
10x5
x2
2x�
55x
3�
10x2
20
x�
10x5
x2
4y
x
13.9
bx�
3bx2
�6x
314
.x3
�x5
�x2
15.a
x2�
8a2 x
5�
4
�6x
3
3bx
2
9bx
x5
x
3�
x2
8a2 x
5
ax2
�4
16.3
x3y
�4x
y2�
x4y2
�y5
17.x
4�
4x3
�7x
5�
1
�x
4 y2
3x
3 y�
4xy
2
y5
�7x
5
x4
4x
3
1
18.�
3x6
�x5
�2x
819
.�15
cx2
�8c
2 x5
�cx
2x8
�3x
6�
x58c
2 x5
�15
cx2
cx
20.2
4x2 y
�12
x3y2
�6x
421
.�15
x3�
10x4
y2�
7xy2
6x4
�12
x3 y
2
24x
2 y10
x4 y
2�
15x
3
7xy
2
Answers (Lesson 8-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
ract
ice
Po
lyn
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-4
8-4
©G
lenc
oe/M
cGra
w-H
ill47
5G
lenc
oe A
lgeb
ra 1
Lesson 8-4
Sta
te w
het
her
eac
h e
xpre
ssio
n i
s a
pol
ynom
ial.
If t
he
exp
ress
ion
is
a p
olyn
omia
l,id
enti
fy i
t as
a m
onom
ial,
a bi
nom
ial,
or a
tri
nom
ial.
1.5m
n�
n2
2.4b
y�
2b�
by3.
�32
yes;
bin
om
ial
yes;
bin
om
ial
yes;
mo
no
mia
l
4.5.
5x2
�3x
�4
6.2c
2�
8c�
9 �
3
yes;
mo
no
mia
ln
oye
s;tr
ino
mia
l
GEO
MET
RYW
rite
a p
olyn
omia
l to
rep
rese
nt
the
area
of
each
sh
aded
reg
ion
.
7.ab
�xy
8.4r
2�
�r2
Fin
d t
he
deg
ree
of e
ach
pol
ynom
ial.
9.12
010
.3r4
411
.b�
61
12.4
a3�
2a3
13.5
abc
�2b
2�
13
14.8
x5y4
�2x
89
Arr
ange
th
e te
rms
of e
ach
pol
ynom
ial
so t
hat
th
e p
ower
s of
xar
e in
asc
end
ing
ord
er.
15.3
x�
1 �
2x2
1
3x
2x2
16.5
x�
6 �
3x2
�6
5x
3x
2
17.9
x2�
2 �
x3�
x2
x
9x
2
x3
18.�
3 �
3x3
�x2
�4x
�3
4x
�x
2
3x3
19.7
r5x
�21
r4�
r2x2
�15
x320
.3a2
x4�
14a2
�10
x3�
ax2
21r4
7r
5 x�
r2x
2�
15x3
14a2
ax
2�
10x3
3a
2 x4
Arr
ange
th
e te
rms
of e
ach
pol
ynom
ial
so t
hat
th
e p
ower
s of
xar
e in
des
cen
din
gor
der
.
21.x
2�
3x3
�27
�x
22.2
5 �
x3�
x
3x3
x2
�x
27
�x3
x
25
23.x
�3x
2�
4 �
5x3
24.x
2�
64 �
x�
7x3
5x3
�3x
2
x
47x
3
x2�
x
64
25.2
cx�
32 �
c3x2
�6x
326
.13
�x3
y3�
x2y2
�x
6x3
�c
3 x2
2c
x
32�
x3y
3
x2y
2
x
13
r
ax
by
3x � 7
©G
lenc
oe/M
cGra
w-H
ill47
6G
lenc
oe A
lgeb
ra 1
Sta
te w
het
her
eac
h e
xpre
ssio
n i
s a
pol
ynom
ial.
If t
he
exp
ress
ion
is
a p
olyn
omia
l,id
enti
fy i
t as
a m
onom
ial,
a bi
nom
ial,
or a
tri
nom
ial.
1.7a
2 b�
3b2
�a2
b2.
y3�
y2�
93.
6g2 h
3 k
yes;
bin
om
ial
yes;
trin
om
ial
yes;
mo
no
mia
l
GEO
MET
RYW
rite
a p
olyn
omia
l to
rep
rese
nt
the
area
of
each
sh
aded
reg
ion
.
4.ab
�b
25.
d2
��
d2
Fin
d t
he
deg
ree
of e
ach
pol
ynom
ial.
6.x
�3x
4�
21x2
�x3
47.
3g2 h
3�
g3h
5
8.�
2x2 y
�3x
y3�
x24
9.5n
3 m�
2m3
�n
2 m4
�n
26
10.a
3 b2 c
�2a
5 c�
b3c2
611
.10s
2 t2
�4s
t2�
5s3 t
25
Arr
ange
th
e te
rms
of e
ach
pol
ynom
ial
so t
hat
th
e p
ower
s of
xar
e in
asc
end
ing
ord
er.
12.8
x2�
15 �
5x5
13.1
0bx
�7b
2�
x4�
4b2 x
3
�15
8x
2
5x5
�7b
2
10b
x
4b2 x
3
x4
14.�
3x3 y
�8y
2�
xy4
15.7
ax�
12 �
3ax3
�a2
x2
8y2
xy
4�
3x3 y
�12
7a
x
a2x2
3a
x3
Arr
ange
th
e te
rms
of e
ach
pol
ynom
ial
so t
hat
th
e p
ower
s of
xar
e in
des
cen
din
gor
der
.
16.1
3x2
�5
�6x
3�
x17
.4x
�2x
5�
6x3
�2
6x3
13
x2�
x�
52x
5�
6x3
4x
2
18.g
2 x�
3gx3
�7g
3�
4x2
19.�
11x2
y3�
6y�
2xy
�2x
4
�3g
x3
4x
2
g2 x
7g
32x
4�
11x
2 y3
�2x
y
6y
20.7
a2x2
�17
�a3
x3�
2ax
21.1
2rx3
�9r
6�
r2x
�8x
6
�a
3 x3
7a
2 x2
2a
x
178x
6
12rx
3
r2x
9r
6
22.M
ON
EYW
rite
a p
olyn
omia
l to
rep
rese
nt
the
valu
e of
tte
n-d
olla
r bi
lls,
ffi
fty-
doll
arbi
lls,
and
hon
e-h
un
dred
-dol
lar
bill
s.10
t
50f
10
0h
23.G
RA
VIT
YT
he
hei
ght
abov
e th
e gr
oun
d of
a b
all
thro
wn
up
wit
h a
vel
ocit
y of
96
feet
per
seco
nd
from
a h
eigh
t of
6 f
eet
is 6
�96
t�
16t2
feet
,wh
ere
tis
th
e ti
me
in s
econ
ds.
Acc
ordi
ng
to t
his
mod
el,h
ow h
igh
is
the
ball
aft
er 7
sec
onds
? E
xpla
in.
�10
6 ft
;Th
e h
eig
ht
is n
egat
ive
bec
ause
th
e m
od
el d
oes
no
t ac
cou
nt
for
the
bal
l hit
tin
g t
he
gro
un
d w
hen
th
e h
eig
ht
is 0
fee
t.1 � 4
dab
b
1 � 5
Pra
ctic
e (
Ave
rag
e)
Po
lyn
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-4
8-4
Answers (Lesson 8-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csP
oly
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-4
8-4
©G
lenc
oe/M
cGra
w-H
ill47
7G
lenc
oe A
lgeb
ra 1
Lesson 8-4
Pre-
Act
ivit
yH
ow a
re p
olyn
omia
ls u
sefu
l in
mod
elin
g d
ata?
Rea
d th
e in
trod
uct
ion
to
Les
son
8-4
at
the
top
of p
age
432
in y
our
text
book
.
•H
ow m
any
term
s do
es t
4�
9t3
�26
t�
18t
�76
hav
e?
five
•W
hat
cou
ld y
ou c
all
a po
lyn
omia
l w
ith
just
on
e te
rm?
a m
on
om
ial
Rea
din
g t
he
Less
on
1.W
hat
is
the
mea
nin
g of
th
e pr
efix
es m
ono-
,bi-
,an
d tr
i-?
Mo
no
- m
ean
s o
ne,
bi-
mea
ns
two
,an
d t
ri-
mea
ns
thre
e.
2.W
rite
exa
mpl
es o
f w
ords
th
at b
egin
wit
h t
he
pref
ixes
mon
o-,b
i-,a
nd
tri-
.
Sam
ple
an
swer
:m
on
ocy
cle
(on
e w
hee
l),b
icyc
le (
two
wh
eels
),tr
icyc
le(t
hre
e w
hee
ls)
3.C
ompl
ete
the
tabl
e. mo
no
mia
lb
ino
mia
ltr
ino
mia
lp
oly
no
mia
l wit
h m
ore
th
an t
hre
e te
rms
Exa
mp
le3r
2 t2x
2�
3x5x
2�
3x�
27s
2�
s4�
2s3
�s
�5
Nu
mb
er o
f Ter
ms
12
35
4.W
hat
is
the
degr
ee o
f th
e m
onom
ial
3xy2
z?4
5.W
hat
is
the
degr
ee o
f th
e po
lyn
omia
l 4x
4�
2x3 y
3�
y2�
14?
Exp
lain
how
you
fou
nd
you
r an
swer
.
6;S
ince
0
4 �
4 ,4
x4
has
deg
ree
4;si
nce
0
3
3 �
6,2x
3 y3
has
deg
ree
6;y
2h
as d
egre
e 2;
and
14
has
deg
ree
0.T
he
hig
hes
t d
egre
e o
fth
ese
term
s is
6.
Hel
pin
g Y
ou
Rem
emb
er
6.U
se a
dic
tion
ary
to f
ind
the
mea
nin
g of
th
e te
rms
asce
nd
ing
and
des
cen
din
g.W
rite
th
eir
mea
nin
gs a
nd
then
des
crib
e a
situ
atio
n i
n y
our
ever
yday
lif
e th
at r
elat
es t
o th
em.
asce
nd
ing
:g
oin
g,g
row
ing
,or
mov
ing
up
war
d;
des
cen
din
g:
mov
ing
fro
ma
hig
her
to
a lo
wer
pla
ce;
Sam
ple
an
swer
:cl
imb
ing
sta
irs,
hik
ing
©G
lenc
oe/M
cGra
w-H
ill47
8G
lenc
oe A
lgeb
ra 1
Po
lyn
om
ial F
un
ctio
ns
Su
ppos
e a
lin
ear
equ
atio
n s
uch
as
23x
�y
�4
is
sol
ved
for
y.T
hen
an
equ
ival
ent
equ
atio
n,
y�
3x�
4,is
fou
nd.
Exp
ress
ed i
n t
his
way
,yis
a
fun
ctio
n o
f x,
or f
(x)
�3x
�4.
Not
ice
that
th
e ri
ght
side
of
the
equ
atio
n i
s a
bin
omia
l of
de
gree
1.
Hig
her
-deg
ree
poly
nom
ials
in
xm
ay a
lso
form
fu
nct
ion
s.A
n e
xam
ple
is f
(x)
�x3
�1,
wh
ich
is
a p
olyn
omia
l fu
nct
ion
of
degr
ee 3
.You
can
gr
aph
th
is f
un
ctio
n u
sin
g a
tabl
e of
ord
ered
pa
irs,
as s
how
n a
t th
e ri
ght.
For
eac
h o
f th
e fo
llow
ing
pol
ynom
ial
fun
ctio
ns,
mak
e a
tab
leof
val
ues
for
xan
d y
�f(
x).T
hen
dra
w t
he
grap
h o
n t
he
grid
.
1.f(
x) �
1 �
x22.
f(x)
�x2
�5
3.f(
x) �
x2�
4x�
14.
f(x)
�x3
x
y
Ox
y
O
x
y
Ox
y
O
x
y
O
xy
�1 �
1 2��
2 �3 8�
�1
0
01
12
1 �1 2�
4�3 8�
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-4
8-4
Answers (Lesson 8-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Add
ing
an
d S
ub
trac
tin
g P
oly
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-5
8-5
©G
lenc
oe/M
cGra
w-H
ill47
9G
lenc
oe A
lgeb
ra 1
Lesson 8-5
Ad
d P
oly
no
mia
lsTo
add
pol
ynom
ials
,you
can
gro
up li
ke t
erm
s ho
rizo
ntal
ly o
r w
rite
them
in
col
um
n f
orm
,ali
gnin
g li
ke t
erm
s ve
rtic
ally
.Lik
e te
rms
are
mon
omia
l te
rms
that
are
eith
er i
den
tica
l or
dif
fer
only
in
th
eir
coef
fici
ents
,su
ch a
s 3p
and
�5p
or 2
x2y
and
8x2 y
.
Fin
d
(2x2
x
�8)
(3
x�
4x2
2)
.
Hor
izon
tal
Met
hod
Gro
up
like
ter
ms.
(2x2
�x
�8)
�(3
x�
4x2
�2)
�[(
2x2
�(�
4x2 )
] �
(x�
3x)
�[(
�8)
�2)
]�
�2x
2�
4x�
6.
Th
e su
m i
s �
2x2
�4x
�6.
Fin
d (
3x2
5x
y)
(xy
2x
2 ).
Ver
tica
l M
eth
odA
lign
lik
e te
rms
in c
olu
mn
s an
d ad
d.
3x2
�5x
y(�
)2x
2�
xyP
ut t
he t
erm
s in
des
cend
ing
orde
r.
5x2
�6x
y
Th
e su
m i
s 5x
2�
6xy.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
su
m.
1.(4
a�
5) �
(3a
�6)
2.(6
x�
9) �
(4x2
�7)
7a
14x
2
6x
2
3.(6
xy�
2y�
6x)
�(4
xy�
x)4.
(x2
�y2
) �
(�x2
�y2
)
10xy
5x
2y
2y2
5.(3
p2�
2p�
3) �
(p2
�7p
�7)
6.(2
x2�
5xy
�4y
2 ) �
(�xy
�6x
2�
2y2 )
4p2
�9p
10
�4x
2
4xy
6y
2
7.(5
p�
2q)
�(2
p2�
8q�
1)8.
(4x2
�x
�4)
�(5
x�
2x2
�2)
2p2
5p
�6q
1
6x2
4x
6
9.(6
x2�
3x)
�(x
2�
4x�
3)10
.(x2
�2x
y�
y2)
�(x
2�
xy�
2y2 )
7x2
�x
�3
2x2
xy
�y2
11.(
2a�
4b�
c) �
(�2a
�b
�4c
)12
.(6x
y2�
4xy)
�(2
xy�
10xy
2�
y2)
�5b
�5c
�4x
y2
6xy
y2
13.(
2p�
5q)
�(3
p�
6q)
�(p
�q)
14.(
2x2
�6)
�(5
x2�
2) �
(�x2
�7)
6p6x
2�
11
15.(
3z2
�5z
) �
(z2
�2z
) �
(z�
4)16
.(8x
2�
4x�
3y2
�y)
�(6
x2�
x�
4y)
4z2
8z�
414
x2
3x
3y2
5y
©G
lenc
oe/M
cGra
w-H
ill48
0G
lenc
oe A
lgeb
ra 1
Sub
trac
t Po
lyn
om
ials
You
can
su
btra
ct a
pol
ynom
ial
by a
ddin
g it
s ad
diti
ve i
nve
rse.
To
fin
d th
e ad
diti
ve i
nve
rse
of a
pol
ynom
ial,
repl
ace
each
ter
m w
ith
its
add
itiv
e in
vers
e or
opp
osit
e.
Fin
d (
3x2
2x
�6)
�(2
x
x2
3).
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Add
ing
an
d S
ub
trac
tin
g P
oly
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-5
8-5
Exam
ple
Exam
ple
Hor
izon
tal
Met
hod
Use
add
itiv
e in
vers
es t
o re
wri
te a
s ad
diti
on.
Th
en g
rou
p li
ke t
erm
s.
(3x2
�2x
�6)
�(2
x�
x2�
3)�
(3x2
�2x
�6)
�[(
�2x
)�(�
x2)
�(�
3)]
�[3
x2�
(�x2
)] �
[2x
�(�
2x)]
�[�
6 �
(�3)
]�
2x2
�(�
9)�
2x2
�9
Th
e di
ffer
ence
is
2x2
�9.
Ver
tica
l M
eth
od
Ali
gn l
ike
term
s in
col
um
ns
and
subt
ract
by
addi
ng
the
addi
tive
in
vers
e.
3x2
�2x
�6
(�)
x2�
2x�
3
3x2
�2x
�6
(�)
�x2
�2x
�3
2x2
�9
Th
e di
ffer
ence
is
2x2
�9.
Exer
cises
Exer
cises
Fin
d e
ach
dif
fere
nce
.
1.(3
a�
5) �
(5a
�1)
2.(9
x�
2) �
(�3x
2�
5)
�2a
�6
3x2
9x
7
3.(9
xy�
y�
2x)
�(6
xy�
2x)
4.(x
2�
y2)
�(�
x2�
y2)
3xy
y
2x2
5.(6
p2�
4p�
5) �
(2p2
�5p
�1)
6.(6
x2�
5xy
�2y
2 ) �
(�xy
�2x
2�
4y2 )
4p2
9p
4
8x2
6x
y
2y2
7.(8
p�
5q)
�(�
6p2
�6q
�3)
8.(8
x2�
4x�
3) �
(�2x
�x2
�5)
6p2
8p
�11
q
39x
2�
2x�
8
9.(3
x2�
2x)
�(3
x2�
5x�
1)10
.(4x
2�
6xy
�2y
2 ) �
(�x2
�2x
y�
5y2 )
�7x
1
5x2
4xy
7y
2
11.(
2h�
6j�
2k)
�(�
7h�
5j�
4k)
12.(
9xy2
�5x
y) �
(�2x
y�
8xy2
)
9h�
j2k
17xy
2
7xy
13.(
2a�
8b)
�(�
3a�
5b)
14.(
2x2
�8)
�(�
2x2
�6)
5a�
13b
4x2
�2
15.(
6z2
�4z
�2)
�(4
z2�
z)16
.(6x
2�
5x�
1) �
(�7x
2�
2x�
4)
2z2
3z
2
13x2
�3x
�3
Answers (Lesson 8-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Add
ing
an
d S
ub
trac
tin
g P
oly
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-5
8-5
©G
lenc
oe/M
cGra
w-H
ill48
1G
lenc
oe A
lgeb
ra 1
Lesson 8-5
Fin
d e
ach
su
m o
r d
iffe
ren
ce.
1.(2
x�
3y)
�(4
x�
9y) 6x
12
y2.
(6s
�5t
) �
(4t
�8s
) 14
s
9t
3.(5
a�
9b)
�(2
a�
4b) 3a
5b
4.(1
1m�
7n)
�(2
m�
6n) 9m
�13
n
5.(m
2�
m)
�(2
m�
m2 )
2m
2
m6.
(x2
�3x
) �
(2x2
�5x
) �
x2�
8x
7.(d
2�
d�
5) �
(2d
�5)
d2
�3d
8.(2
e2�
5e)
�(7
e�
3e2 )
�e2
2e
9.(5
f�
g�
2) �
(�2f
�3)
10.(
6k2
�2k
�9)
�(4
k2�
5k)
3f
g
110
k2
�3k
9
11.(
x3�
x�
1) �
(3x
�1)
12.(
b2�
ab�
2) �
(2b2
�2a
b)
x3
�4x
2
�b
2�
ab�
2
13.(
7z2
�4
�z)
�(�
5 �
3z2 )
14.(
5 �
4n�
2m)
�(�
6m�
8)
4z2
�z
9
�3
4n
�4m
15.(
4t2
�2)
�(�
4 �
2t)
16.(
3g3
�7g
) �
(4g
�8g
3 )
4t2
2t
�2
�5g
3
3g
17.(
2a2
�8a
�4)
�(a
2�
3)18
.(3x
2�
7x�
5) �
(�x2
�4x
)
a2
8a
74x
2�
11x
5
19.(
7z2
�z
�1)
�(�
4z�
3z2
�3)
20.(
2c2
�7c
�4)
�(c
2�
1 �
9c)
4z2
5z
4
3c2
�2c
5
21.(
n2
�3n
�2)
�(2
n2
�6n
�2)
22.(
a2�
ab�
3b2 )
�(b
2�
4a2
�ab
)
�n
2
9n
45a
2�
2b2
23.(
�2�
5��
6) �
(2�2
�5
��)
24.(
2m2
�5m
�1)
�(4
m2
�3m
�3)
3�2
�4
��
1�
2m2
8m
4
25.(
x2�
6x�
2) �
(�5x
2�
7x�
4)26
.(5b
2�
9b�
5) �
(b2
�6
�2b
)
6x2
�13
x
66b
2�
7b�
11
27.(
2x2
�6x
�2)
�(x
2�
4x)
�(3
x2�
x�
5)6x
2�
x
3
©G
lenc
oe/M
cGra
w-H
ill48
2G
lenc
oe A
lgeb
ra 1
Fin
d e
ach
su
m o
r d
iffe
ren
ce.
1.(4
y�
5) �
(�7y
�1)
2.(�
x2�
3x)
�(5
x�
2x2 )
�3y
4
�3x
2�
2x
3.(4
k2�
8k�
2) �
(2k
�3)
4.(2
m2
�6m
) �
(m2
�5m
�7)
4k2
6k
�1
3m2
m
7
5.(2
w2
�3w
�1)
�(4
w�
7)6.
(g3
�2g
2 ) �
(6g
�4g
2�
2g3 )
2w2
w
�6
�g
3
6g2
�6g
7.(5
a2�
6a�
2) �
(7a2
�7a
�5)
8.(�
4p2
�p
�9)
�(p
2�
3p�
1)�
2a2
13
a�
3�
3p2
2p
8
9.(x
3�
3x�
1) �
(x3
�7
�12
x)10
.(6c
2�
c�
1) �
(�4
�2c
2�
8c)
9x�
64c
2�
9c
5
11.(
�b3
�8b
c2�
5) �
(7bc
2�
2 �
b3)
12.(
5n2
�3n
�2)
�(�
n�
2n2
�4)
�2b
3
bc
2
77n
2�
4n�
2
13.(
4y2
�2y
�8)
�(7
y2�
4 �
y)14
.(w
2�
4w�
1) �
(�5
�5w
2�
3w)
�3y
2
3y�
126w
2�
7w�
6
15.(
4u2
�2u
�3)
�(3
u2
�u
�4)
16.(
5b2
�8
�2b
) �
(b�
9b2
�5)
7u2
�3u
1
�4b
2
b�
13
17.(
4d2
�2d
�2)
�(5
d2
�2
�d
)18
.(8x
2�
x�
6) �
(�x2
�2x
�3)
9d2
d
9x2
�x
�3
19.(
3h2
�7h
�1)
�(4
h�
8h2
�1)
20.(
4m2
�3m
�10
) �
(m2
�m
�2)
�5h
2
3h�
25m
2�
2m
8
21.(
x2�
y2�
6) �
(5x2
�y2
�5)
22.(
7t2
�2
�t)
�(t
2�
7 �
2t)
�4x
2
2y2
�1
8t2
�3t
�5
23.(
k3�
2k2
�4k
�6)
�(�
4k�
k2�
3)24
.(9j
2�
j�
jk)
�(�
3j2
�jk
�4j
)k
3�
3k2
8k
9
6j2
�3j
25.(
2x�
6y�
3z)
�(4
x�
6z�
8y)
�(x
�3y
�z)
7x�
5y
4z
26.(
6f2
�7f
�3)
�(5
f2�
1 �
2f)
�(2
f2�
3 �
f)�
f2�
10f
1
27.B
USI
NES
ST
he
poly
nom
ial
s3�
70s2
�15
00s
�10
,800
mod
els
the
prof
it a
com
pan
ym
akes
on
sel
lin
g an
ite
m a
t a
pric
e s.
A s
econ
d it
em s
old
at t
he
sam
e pr
ice
brin
gs i
n a
prof
it o
f s3
�30
s2�
450s
�50
00.W
rite
a p
olyn
omia
l th
at e
xpre
sses
th
e to
tal
prof
itfr
om t
he
sale
of
both
ite
ms.
2s3
�10
0s2
19
50s
�15
,800
28.G
EOM
ETRY
Th
e m
easu
res
of t
wo
side
s of
a t
rian
gle
are
give
n.
If P
is t
he
peri
met
er,a
nd
P�
10x
�5y
,fin
d th
e m
easu
re o
f th
e th
ird
side
.2x
2y
3x
4y
5x �
y
Pra
ctic
e (
Ave
rag
e)
Add
ing
an
d S
ub
trac
tin
g P
oly
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-5
8-5
Answers (Lesson 8-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csA
ddin
g a
nd
Su
btr
acti
ng
Po
lyn
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-5
8-5
©G
lenc
oe/M
cGra
w-H
ill48
3G
lenc
oe A
lgeb
ra 1
Lesson 8-5
Pre-
Act
ivit
yH
ow c
an a
dd
ing
pol
ynom
ials
hel
p y
ou m
odel
sal
es?
Rea
d th
e in
trod
uct
ion
to
Les
son
8-5
at
the
top
of p
age
439
in y
our
text
book
.
Wh
at o
pera
tion
wou
ld y
ou u
se t
o fi
nd
how
mu
ch m
ore
the
trad
itio
nal
toy
sale
s R
wer
e th
an t
he
vide
o ga
mes
sal
es V
?
sub
trac
tio
n
Rea
din
g t
he
Less
on
1.U
se t
he
exam
ple
(�3x
3�
4x2
�5x
�1)
�(�
5x3
�2x
2�
2x�
7).
a.S
how
wh
at i
s m
ean
t by
gro
upi
ng
like
ter
ms
hor
izon
tall
y.
[�3x
3
(�5x
3 )]
[(
4x2
(�
2x2 )
]
(5x
2x
)
[1
(�7)
]
b.
Sh
ow w
hat
is
mea
nt
by a
lign
ing
like
ter
ms
vert
ical
ly.
�3x
3
4x2
5x
1
()
�5x
3�
2x2
2x
�7
c.C
hoo
se o
ne
met
hod
,th
en a
dd t
he
poly
nom
ials
.
�8x
3
2x2
7x
�6
2.H
ow i
s su
btra
ctin
g a
poly
nom
ial
like
su
btra
ctin
g a
rati
onal
nu
mbe
r?
You
su
btr
act
by a
dd
ing
th
e ad
dit
ive
inve
rse.
3.A
n a
lgeb
ra s
tude
nt
got
the
foll
owin
g ex
erci
se w
ron
g on
his
hom
ewor
k.W
hat
was
h
is e
rror
?
(3x5
�3x
4�
2x3
�4x
2�
5) �
(2x5
�x3
�2x
2�
4)�
[3x5
�(�
2x5 )
] �
(�3x
4 ) �
[2x3
�(�
x3)]
�[�
4x2
�(�
2x2 )
] �
(5 �
4)�
x5�
3x4
�x3
�6x
2�
9
He
did
no
t ad
d t
he
add
itiv
e in
vers
e o
f �
x3 .
Hel
pin
g Y
ou
Rem
emb
er
4.H
ow i
s ad
din
g an
d su
btra
ctin
g po
lyn
omia
ls v
erti
call
y li
ke a
ddin
g an
d su
btra
ctin
gde
cim
als
vert
ical
ly?
Alig
nin
g li
ke t
erm
s w
hen
ad
din
g o
r su
btr
acti
ng
po
lyn
om
ials
is li
ke u
sin
gp
lace
val
ue
to a
lign
dig
its
wh
en y
ou
ad
d o
r su
btr
act
dec
imal
s.
©G
lenc
oe/M
cGra
w-H
ill48
4G
lenc
oe A
lgeb
ra 1
Cir
cula
r A
reas
an
d V
olu
mes
Are
a of
Cir
cle
Vol
um
e of
Cyl
ind
erV
olu
me
of C
one
A�
�r2
V�
�r2
hV
��
r2h
Wri
te a
n a
lgeb
raic
exp
ress
ion
for
eac
h s
had
ed a
rea.
(Rec
all
that
th
e d
iam
eter
of
a ci
rcle
is
twic
e it
s ra
diu
s.)
1.2.
3.
�x2
���
�2�
�x2
(y2
2x
y)�
x2
Wri
te a
n a
lgeb
raic
exp
ress
ion
for
th
e to
tal
volu
me
of e
ach
fig
ure
.
4.5.
5�
x3
[13x
3
(4a
9b
)x2 ]
Eac
h f
igu
re h
as a
cyl
ind
rica
l h
ole
wit
h a
rad
ius
of 2
in
ches
an
d
a h
eigh
t of
5 i
nch
es.F
ind
eac
h v
olu
me.
6.7.
x3
�20
�in
33�
x3
�20
�in
317
5��
4
3x
4x
5x
7x
� � 122 � 3
3x — 2
x
a
x
x
b
x
2x5x
19 � 2� � 2
x � 2
3x2x
2xx
yx
xy
x
x
r
h
r
h
r
1 � 3
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-5
8-5
Answers (Lesson 8-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Mu
ltip
lyin
g a
Po
lyn
om
ial b
y a
Mo
no
mia
l
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-6
8-6
©G
lenc
oe/M
cGra
w-H
ill48
5G
lenc
oe A
lgeb
ra 1
Lesson 8-6
Pro
du
ct o
f M
on
om
ial a
nd
Po
lyn
om
ial
Th
e D
istr
ibu
tive
Pro
pert
y ca
n b
e u
sed
tom
ult
iply
a p
olyn
omia
l by
a m
onom
ial.
You
can
mu
ltip
ly h
oriz
onta
lly
or v
erti
call
y.S
omet
imes
mu
ltip
lyin
g re
sult
s in
lik
e te
rms.
Th
e pr
odu
cts
can
be
sim
plif
ied
by c
ombi
nin
g li
ke t
erm
s.
Fin
d �
3x2 (
4x2
�6x
�8)
.
Hor
izon
tal
Met
hod
�3x
2 (4x
2�
6x�
8)�
�3x
2 (4x
2 ) �
(�3x
2 )(6
x) �
(�3x
2 )(8
)�
�12
x4�
(�18
x3)
�(�
24x2
)�
�12
x4�
18x3
�24
x2
Ver
tica
l M
eth
od4x
2�
6x�
8(�
) �
3x2
�12
x4�
18x3
�24
x2
Th
e pr
odu
ct i
s �
12x4
�18
x3�
24x2
.
Sim
pli
fy �
2(4x
2�
5x)
�x
(x2
�6x
).
�2(
4x2
�5x
) �
x( x
2�
6x)
��
2(4x
2 ) �
(�2)
(5x)
�(�
x)(x
2 ) �
(�x)
(6x)
��
8x2
�(�
10x)
�(�
x3)
�(�
6x2 )
�(�
x3)
�[�
8x2
�(�
6x2 )
] �
(�10
x)�
�x3
�14
x2�
10x
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
pro
du
ct.
1.x(
5x�
x2)
2.x(
4x2
�3x
�2)
3.�
2xy(
2y�
4x2 )
5x2 �
x3
4x3 �
3x2 �
2x�
4xy
2�
8x3 y
4.�
2g(g
2�
2g�
2)5.
3x(x
4�
x3�
x2)
6.�
4x(2
x3�
2x�
3)
�2g
3�
4g2
�4g
3x5
�3x
4�
3x3
�8x
4 �8x
2 �12
x
7.�
4cx(
10 �
3x)
8.3y
(�4x
�6x
3 �2y
)9.
2x2 y
2 (3x
y�
2y�
5x)
�40
cx�
12cx
2�
12xy
�18
x3 y
�6y
26x
3 y3
�4x
2 y3
�10
x3 y
2
Sim
pli
fy.
10.x
(3x
�4)
�5x
11.�
x(2x
2�
4x)
�6x
2
3x2
�9x
�2x
3�
2x2
12.6
a(2a
�b)
�2a
(�4a
�5b
)13
.4r(
2r2
�3r
�5)
�6r
(4r2
�2r
�8)
4a2
�4a
b32
r3�
68r
14.4
n(3
n2
�n
�4)
�n
(3 �
n)
15.2
b(b2
�4b
�8)
�3b
(3b2
�9b
�18
)
12n
3�
5n2
�19
n�
7b3
�19
b2
�70
b
16.�
2z(4
z2�
3z�
1) �
z(3z
2�
2z�
1)17
.2(4
x2�
2x)
�3(
�6x
2�
4) �
2x(x
�1)
�11
z3
�4z
2�
z28
x2
�6x
�12
©G
lenc
oe/M
cGra
w-H
ill48
6G
lenc
oe A
lgeb
ra 1
Solv
e Eq
uat
ion
s w
ith
Po
lyn
om
ial E
xpre
ssio
ns
Man
y eq
uat
ion
s co
nta
inpo
lyn
omia
ls t
hat
mu
st b
e ad
ded,
subt
ract
ed,o
r m
ult
ipli
ed b
efor
e th
e eq
uat
ion
can
be
solv
ed.
Sol
ve 4
(n�
2) �
5n�
6(3
�n
) �
19.
4(n
�2)
�5n
�6(
3 �
n)
�19
Orig
inal
equ
atio
n
4n�
8 �
5n�
18 �
6n�
19D
istr
ibut
ive
Pro
pert
y
9n�
8 �
37 �
6nC
ombi
ne li
ke t
erm
s.
15n
�8
�37
Add
6n
to b
oth
side
s.
15n
�45
Add
8 t
o bo
th s
ides
.
n�
3D
ivid
e ea
ch s
ide
by 1
5.
Th
e so
luti
on i
s 3.
Sol
ve e
ach
eq
uat
ion
.
1.2(
a�
3) �
3(�
2a�
6)3
2.3(
x�
5) �
6 �
183
3.3x
(x�
5) �
3x2
��
302
4.6(
x2�
2x)
�2(
3x2
�12
)2
5.4(
2p�
1) �
12p
�2(
8p�
12)
�1
6.2(
6x�
4) �
2 �
4(x
�4)
�3
7.�
2(4y
�3)
�8y
�6
�4(
y�
2)1
8.c(
c�
2) �
c(c
�6)
�10
c�
126
9.3(
x2�
2x)
�3x
2�
5x�
111
10.2
(4x
�3)
�2
��
4(x
�1)
�1
11.3
(2h
�6)
�(2
h�
1) �
97
12.3
(y�
5) �
(4y
�8)
��
2y�
10�
13
13.3
(2a
�6)
�(�
3a�
1) �
4a�
22
14.5
(2x2
�1)
�(1
0x2
�6)
��
(x�
2)�
3
15.3
(x�
2) �
2(x
�1)
��
5(x
�3)
16.4
(3p2
�2p
) �
12p2
�2(
8p�
6)�
3 � 27 � 10
1 �
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Mu
ltip
lyin
g a
Po
lyn
om
ial b
y a
Mo
no
mia
l
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-6
8-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
3 � 5
Answers (Lesson 8-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
ract
ice
Mu
ltip
lyin
g a
Po
lyn
om
ial b
y a
Mo
no
mia
l
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-6
8-6
©G
lenc
oe/M
cGra
w-H
ill48
7G
lenc
oe A
lgeb
ra 1
Lesson 8-6
Fin
d e
ach
pro
du
ct.
1.a(
4a�
3)2.
�c(
11c
�4)
4a2
3a
�11
c2
�4c
3.x(
2x�
5)4.
2y(y
�4)
2x2
�5x
2y2
�8y
5.�
3n(n
2�
2n)
6.4h
(3h
�5)
�3n
3�
6n2
12h
2�
20h
7.3x
(5x2
�x
�4)
8.7c
(5 �
2c2
�c3
)
15x3
�3x
2
12x
35c
�14
c3
7c4
9.�
4b(1
�9b
�2b
2 )10
.6y(
�5
�y
�4y
2 )
�4b
36
b2
8b
3�
30y
�6y
2
24y
3
11.2
m2 (
2m2
�3m
�5)
12.�
3n2 (
�2n
2�
3n�
4)
4m4
6m
3�
10m
26n
4�
9n3
�12
n2
Sim
pli
fy.
13.w
(3w
�2)
�5w
14.f
(5f
�3)
�2f
3w2
7w
5f2
�5f
15.�
p(2p
�8)
�5p
16.y
2 (�
4y�
5) �
6y2
�2p
2
3p�
4y3
�y
2
17.2
x(3x
2�
4) �
3x3
18.4
a(5a
2�
4) �
9a
3x3
8x
20a3
�7a
19.4
b(�
5b�
3) �
2(b2
�7b
�4)
20.3
m(3
m�
6) �
3(m
2�
4m�
1)
�22
b2
2b
8
6m2
6m
�3
Sol
ve e
ach
eq
uat
ion
.
21.3
(a�
2) �
5 �
2a�
4�
722
.2(4
x�
2) �
8 �
4(x
�3)
4
23.5
(y�
1) �
2 �
4(y
�2)
�6
�5
24.4
(b�
6) �
2(b
�5)
�2
�6
25.6
(m�
2) �
14 �
3(m
�2)
�10
�2
26.3
(c�
5) �
2 �
2(c
�6)
�2
1
©G
lenc
oe/M
cGra
w-H
ill48
8G
lenc
oe A
lgeb
ra 1
Fin
d e
ach
pro
du
ct.
1.2h
(�7h
2�
4h)
2.6p
q(3p
2�
4q)
3.�
2u2 n
(4u
�2n
)�
14h
3�
8h2
18p
3 q
24p
q2
�8u
3 n
4u2 n
2
4.5j
k(3j
k�
2k)
5.�
3rs(
�2s
2�
3r)
6.4m
g2(2
mg
�4g
)15
j2k
2
10jk
26r
s3�
9r2 s
8m2 g
3
16m
g3
7.�
m(8
m2
�m
�7)
8.�
n2 (
�9n
2�
3n�
6)
�2m
3�
m2
m
6n4
�2n
3�
4n2
Sim
pli
fy.
9.�
2�(3
��
4) �
7�10
.5w
(�7w
�3)
�2w
(�2w
2�
19w
�2)
�6�
2
15�
�4w
3
3w2
19
w
11.6
t(2t
�3)
�5(
2t2
�9t
�3)
12.�
2(3m
3�
5m�
6) �
3m(2
m2
�3m
�1)
2t2
�63
t
159m
2�
7m�
12
13.�
3g(7
g�
2) �
3(g2
�2g
�1)
�3g
(�5g
�3)
�3g
2
3g
3
14.4
z2(z
�7)
�5z
(z2
�2z
�2)
�3z
(4z
�2)
�z3
�6z
2
4z
Sol
ve e
ach
eq
uat
ion
.
15.5
(2s
�1)
�3
�3(
3s�
2)8
16.3
(3u
�2)
�5
�2(
2u�
2)�
3
17.4
(8n
�3)
�5
�2(
6n�
8) �
118
.8(3
b�
1) �
4(b
�3)
�9
�
19.h
(h�
3) �
2h�
h(h
�2)
�12
420
.w(w
�6)
�4w
��
7 �
w(w
�9)
�7
21.t
(t�
4) �
1 �
t(t
�2)
�2
22.u
(u�
5) �
8u�
u(u
�2)
�4
�4
23.N
UM
BER
TH
EORY
Let
xbe
an
in
tege
r.W
hat
is
the
prod
uct
of
twic
e th
e in
tege
r ad
ded
to t
hre
e ti
mes
th
e n
ext
con
secu
tive
in
tege
r?5x
3
INV
ESTM
ENTS
For
Exe
rcis
es 2
4–26
,use
th
e fo
llow
ing
info
rmat
ion
.K
ent
inve
sted
$5,
000
in a
ret
irem
ent
plan
.He
allo
cate
d x
doll
ars
of t
he
mon
ey t
o a
bon
dac
cou
nt
that
ear
ns
4% i
nte
rest
per
yea
r an
d th
e re
st t
o a
trad
itio
nal
acc
oun
t th
at e
arn
s 5%
inte
rest
per
yea
r.
24.W
rite
an
exp
ress
ion
th
at r
epre
sen
ts t
he
amou
nt
of m
oney
in
vest
ed i
n t
he
trad
itio
nal
acco
un
t.5,
000
�x
25.W
rite
a p
olyn
omia
l m
odel
in
sim
ples
t fo
rm f
or t
he
tota
l am
oun
t of
mon
ey T
Ken
t h
asin
vest
ed a
fter
on
e ye
ar.(
Hin
t:E
ach
acc
oun
t h
as A
�IA
doll
ars,
wh
ere
Ais
th
e or
igin
alam
oun
t in
th
e ac
cou
nt
and
Iis
its
in
tere
st r
ate.
)T
�5,
250
�0.
01x
26.I
f K
ent
put
$500
in
th
e bo
nd
acco
un
t,h
ow m
uch
mon
ey d
oes
he
hav
e in
his
ret
irem
ent
plan
aft
er o
ne
year
?$5
,245
3 � 2
1 � 41 � 2
7 � 41 � 4
2 � 31 � 4
Pra
ctic
e (
Ave
rag
e)
Mu
ltip
lyin
g a
Po
lyn
om
ial b
y a
Mo
no
mia
l
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-6
8-6
Answers (Lesson 8-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csM
ult
iply
ing
a P
oly
no
mia
l by
a M
on
om
ial
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-6
8-6
©G
lenc
oe/M
cGra
w-H
ill48
9G
lenc
oe A
lgeb
ra 1
Lesson 8-6
Pre-
Act
ivit
yH
ow i
s fi
nd
ing
the
pro
du
ct o
f a
mon
omia
l an
d a
pol
ynom
ial
rela
ted
to f
ind
ing
the
area
of
a re
ctan
gle?
Rea
d th
e in
trod
uct
ion
to
Les
son
8-6
at
the
top
of p
age
444
in y
our
text
book
.
You
may
rec
all
that
th
e fo
rmu
la f
or t
he
area
of
a re
ctan
gle
is A
��w
.In
this
rec
tan
gle,
��
and
w�
.How
wou
ld y
ou
subs
titu
te t
hes
e va
lues
in
th
e ar
ea f
orm
ula
?
A�
(x
3)(2
x)
Rea
din
g t
he
Less
on
1.R
efer
to
Les
son
8-6
.
a.H
ow i
s th
e D
istr
ibu
tive
Pro
pert
y u
sed
to m
ult
iply
a p
olyn
omia
l by
a m
onom
ial?
Th
e m
on
om
ial i
s m
ult
iplie
d b
y ea
ch t
erm
in t
he
po
lyn
om
ial.
b.
Use
th
e D
istr
ibu
tive
Pro
pert
y to
com
plet
e th
e fo
llow
ing.
2y2 (
3y2
�2y
�7)
�2y
2 ()
�2y
2 ()
�2y
2 ()
��
�
�3x
3 (x3
�2x
2�
3)�
��
��
�
2.W
hat
is
the
diff
eren
ce b
etw
een
sim
plif
yin
g an
exp
ress
ion
an
d so
lvin
g an
equ
atio
n?
Sim
plif
yin
g a
n e
xpre
ssio
n is
co
mb
inin
g li
ke t
erm
s.S
olv
ing
an
eq
uat
ion
is f
ind
ing
th
e va
lue
of
the
vari
able
th
at m
akes
th
e eq
uat
ion
tru
e.
Hel
pin
g Y
ou
Rem
emb
er
3.U
se t
he
equ
atio
n 2
x(x
�5)
�3x
(x�
3) �
5x(x
�7)
�9
to s
how
how
you
wou
ld e
xpla
inth
e pr
oces
s of
sol
vin
g eq
uat
ion
s w
ith
pol
ynom
ial
expr
essi
ons
to a
not
her
alg
ebra
stu
den
t.
Use
th
e D
istr
ibu
tive
Pro
per
ty.
2x2
�10
x
3x2
9x
�5x
2
35x
�9
Co
mb
ine
like
term
s.5 x
2�
x�
5x2
35
x�
9
Su
btr
act
5 x2
fro
m b
oth
sid
es.
�x
�35
x�
9
Su
btr
act
35x
fro
m b
oth
sid
es.
�36
x�
�9
Div
ide
each
sid
e by
�36
.x
�0.
25
9x3
6x5
�3x
6
(�3x
3 )(3
)(�
3x3 )
(2x
2 )�
3x3 (
x3 )
14y
24y
36y
4
72y
3y2
2xx
3
©G
lenc
oe/M
cGra
w-H
ill49
0G
lenc
oe A
lgeb
ra 1
Fig
ura
te N
um
ber
sT
he
nu
mbe
rs b
elow
are
cal
led
pen
tago
nal
nu
mb
ers.
Th
ey a
re t
he
nu
mbe
rs o
f do
ts o
r di
sks
that
can
be
arra
nge
d as
pen
tago
ns.
1.F
ind
the
prod
uct
n
(3n
�1)
.�
2.E
valu
ate
the
prod
uct
in
Exe
rcis
e 1
for
valu
es o
f n
from
1 t
hro
ugh
4.
1,5,
12,2
2
3.W
hat
do
you
not
ice?
Th
ey a
re t
he
firs
t fo
ur
pen
tag
on
al n
um
ber
s.
4.F
ind
the
nex
t si
x pe
nta
gon
al n
um
bers
.35
,51,
70,9
2,11
7,14
5
5.F
ind
the
prod
uct
n
(n�
1).
6.E
valu
ate
the
prod
uct
in
Exe
rcis
e 5
for
valu
es o
f n
from
1 t
hro
ugh
5.O
n a
not
her
sh
eet
ofpa
per,
mak
e dr
awin
gs t
o sh
ow w
hy
thes
e n
um
bers
are
cal
led
the
tria
ngu
lar
nu
mbe
rs.
1,3,
6,10
,15
7.F
ind
the
prod
uct
n(2
n�
1).
2n2
�n
8.E
valu
ate
the
prod
uct
in
Exe
rcis
e 7
for
valu
es o
f n
from
1 t
hro
ugh
5.D
raw
th
ese
hex
agon
al n
um
bers
.1,
6,15
,28,
45
9.F
ind
the
firs
t 5
squ
are
nu
mbe
rs.A
lso,
wri
te t
he
gen
eral
exp
ress
ion
for
an
y sq
uar
en
um
ber.
1,4,
9,16
,25;
n2
Th
e n
um
bers
you
hav
e ex
plor
ed a
bove
are
cal
led
the
plan
e fi
gura
te n
um
bers
bec
ause
th
eyca
n b
e ar
ran
ged
to m
ake
geom
etri
c fi
gure
s.Yo
u c
an a
lso
crea
te s
olid
fig
ura
te n
um
bers
.
10.I
f yo
u p
ile
10 o
ran
ges
into
a p
yram
id w
ith
a t
rian
gle
as a
bas
e,yo
u g
et o
ne
of t
he
tetr
ahed
ral
nu
mbe
rs.H
ow m
any
laye
rs a
re t
her
e in
th
e py
ram
id?
How
man
y or
ange
sar
e th
ere
in t
he
bott
om l
ayer
s?3
laye
rs;
6
11.E
valu
ate
the
expr
essi
on
n3
�n
2�
nfo
r va
lues
of
nfr
om 1
th
rou
gh 5
to
fin
d th
e
firs
t fi
ve t
etra
hed
ral
nu
mbe
rs.
1,4,
10,2
0,35
1 � 31 � 2
1 � 6
n � 2n
2� 2
1 � 2
n � 23 n
2�
21 � 2
●●
2212
51
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-6
8-6
Answers (Lesson 8-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Mu
ltip
lyin
g P
oly
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-7
8-7
©G
lenc
oe/M
cGra
w-H
ill49
1G
lenc
oe A
lgeb
ra 1
Lesson 8-7
Mu
ltip
ly B
ino
mia
lsT
o m
ult
iply
tw
o bi
nom
ials
,you
can
app
ly t
he
Dis
trib
uti
ve P
rope
rty
twic
e.A
use
ful
way
to
keep
tra
ck o
f te
rms
in t
he
prod
uct
is
to u
se t
he
FO
IL m
eth
od a
sil
lust
rate
d in
Exa
mpl
e 2.
Fin
d (
x
3)(x
�4)
.
Hor
izon
tal
Met
hod
(x�
3)(x
�4)
�x(
x�
4) �
3(x
�4)
�(x
)(x)
�x(
�4)
�3(
x)�
3(�
4)�
x2�
4x�
3x�
12�
x2�
x�
12
Ver
tica
l M
eth
od
x�
3(�
) x
�4
�4x
�12
x2�
3xx2
�x
�12
Th
e pr
odu
ct i
s x2
�x
�12
.
Fin
d (
x�
2)(x
5)
usi
ng
the
FO
IL m
eth
od.
(x�
2)(x
�5)
Firs
t O
uter
In
ner
Last
�(x
)(x)
�(x
)(5)
�(�
2)(x
) �
(�2)
(5)
�x2
�5x
�(�
2x)
�10
�x2
�3x
�10
Th
e pr
odu
ct i
s x2
�3x
�10
.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
pro
du
ct.
1.(x
�2)
(x�
3)2.
(x�
4)(x
�1)
3.(x
�6)
(x�
2)
x2
5x
6x2
�3x
�4
x2�
8x
12
4.(p
�4)
(p�
2)5.
(y�
5)(y
�2)
6.(2
x�
1)(x
�5)
p2
�2p
�8
y2
7y
102x
2
9x�
5
7.(3
n�
4)(3
n�
4)8.
(8m
�2)
(8m
�2)
9.(k
�4)
(5k
�1)
9n2
�24
n
1664
m2
�4
5k2
19
k�
4
10.(
3x�
1)(4
x�
3)11
.(x
�8)
(�3x
�1)
12.(
5t�
4)(2
t�
6)
12x2
13
x
3�
3x2
25
x�
810
t2�
22t
�24
13.(
5m�
3n)(
4m�
2n)
14.(
a�
3b)(
2a�
5b)
15.(
8x�
5)(8
x�
5)
20m
2�
22m
n
6n2
2a2
�11
ab
15b
264
x2�
25
16.(
2n�
4)(2
n�
5)17
.(4m
�3)
(5m
�5)
18.(
7g�
4)(7
g�
4)
4n2
2n
�20
20m
2�
35m
15
49g
2�
16
©G
lenc
oe/M
cGra
w-H
ill49
2G
lenc
oe A
lgeb
ra 1
Mu
ltip
ly P
oly
no
mia
lsT
he
Dis
trib
uti
ve P
rope
rty
can
be
use
d to
mu
ltip
ly a
ny
two
poly
nom
ials
. Fin
d (
3x
2)(2
x2�
4x
5).
(3x
�2)
(2x2
�4x
�5)
�3x
(2x2
�4x
�5)
�2(
2x2
�4x
�5)
Dis
trib
utiv
e P
rope
rty
�6x
3�
12x2
�15
x�
4x2
�8x
�10
Dis
trib
utiv
e P
rope
rty
�6x
3�
8x2
�7x
�10
Com
bine
like
ter
ms.
Th
e pr
odu
ct i
s 6x
3�
8x2
�7x
�10
.
Fin
d e
ach
pro
du
ct.
1.(x
�2)
(x2
�2x
�1)
2.(x
�3)
(2x2
�x
�3)
x3
�3x
2
2x3
7x
2�
9
3.(2
x�
1)(x
2�
x�
2)4.
(p�
3)(p
2�
4p�
2)
2x3
�3x
2
5x�
2p
3�
7p2
14
p�
6
5.(3
k�
2)(k
2�
k�
4)6.
(2t
�1)
(10t
2�
2t�
4)
3k3
5k
2�
10k
�8
20t3
6t
2�
10t
�4
7.(3
n�
4)(n
2�
5n�
4)8.
(8x
�2)
(3x2
�2x
�1)
3n3
11
n2
�32
n
1624
x3
10
x2�
12x
2
9.(2
a�
4)(2
a2�
8a�
3)10
.(3x
�4)
(2x2
�3x
�3)
4a3
�8a
2�
26a
12
6x3
x2
�3x
�12
11.(
n2
�2n
�1)
(n2
�n
�2)
12.(
t2�
4t�
1)(2
t2�
t�
3)
n4
3n
3
3n2
3n
�2
2t4
7t
3�
9t2
�11
t
3
13.(
y2�
5y�
3)(2
y2�
7y�
4)14
.(3b
2�
2b�
1)(2
b2�
3b�
4)
2y4
�3y
3�
33y
2
41y
�12
6b4
�13
b3
�4b
2
5b�
4
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Mu
ltip
lyin
g P
oly
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-7
8-7
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 8-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Mu
ltip
lyin
g P
oly
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-7
8-7
©G
lenc
oe/M
cGra
w-H
ill49
3G
lenc
oe A
lgeb
ra 1
Lesson 8-7
Fin
d e
ach
pro
du
ct.
1.(m
�4)
(m�
1)2.
(x�
2)(x
�2)
m2
5m
4
x2
4x
4
3.(b
�3)
(b�
4)4.
(t�
4)(t
�3)
b2
7b
12
t2
t�
12
5.(r
�1)
(r�
2)6.
(z�
5)(z
�1)
r2�
r�
2z2
�4z
�5
7.(3
c�
1)(c
�2)
8.(2
x�
6)(x
�3)
3c2
�5c
�2
2x2
�18
9.(d
�1)
(5d
�4)
10.(
2��
5)(�
�4)
5d2
�9d
4
2�2
�3�
�20
11.(
3n�
7)(n
�3)
12.(
q�
5)(5
q�
1)
3n2
2n
�21
5q2
24
q�
5
13.(
3b�
3)(3
b�
2)14
.(2m
�2)
(3m
�3)
9b2
3b
�6
6m2
�6
15.(
4c�
1)(2
c�
1)16
.(5a
�2)
(2a
�3)
8c2
6c
1
10a2
�19
a
6
17.(
4h�
2)(4
h�
1)18
.(x
�y)
(2x
�y)
16h
2�
12h
2
2x2
�3x
y
y2
19.(
e�
4)(e
2�
3e�
6)20
.(t
�1)
(t2
�2t
�4)
e3
7e2
6e
�24
t3
3t2
6t
4
21.(
k�
4)(k
2�
3k�
6)22
.(m
�3)
(m2
�3m
�5)
k3
7k
2
6k�
24m
3
6m2
14
m
15
GE
OM
ET
RY
Wri
te a
n e
xpre
ssio
n t
o re
pre
sen
t th
e ar
ea o
f ea
ch f
igu
re.
23.
24.
8x2
18
x�
5 u
nit
s2(x
2
4x
4)�
un
its2
2x
4
2x
5
4x �
1
©G
lenc
oe/M
cGra
w-H
ill49
4G
lenc
oe A
lgeb
ra 1
Fin
d e
ach
pro
du
ct.
1.(q
�6)
(q�
5)2.
(x�
7)(x
�4)
3.(s
�5)
(s�
6)q
2
11q
30
x2
11x
28
s2�
s�
30
4.(n
�4)
(n�
6)5.
(a�
5)(a
�8)
6.(w
�6)
(w�
9)n
2�
10n
24
a2�
13a
40
w2
�15
w
54
7.(4
c�
6)(c
�4)
8.(2
x�
9)(2
x�
4)9.
(4d
�5)
(2d
�3)
4c2
�10
c�
244x
2�
10x
�36
8d2
�22
d
15
10.(
4b�
3)(3
b�
4)11
.(4m
�2)
(4m
�3)
12.(
5c�
5)(7
c�
9)12
b2
�7b
�12
16m
2�
4m�
635
c2
10
c�
45
13.(
6a�
3)(7
a�
4)14
.(6h
�3)
(4h
�2)
15.(
2x�
2)(5
x�
4)42
a2
�45
a
1224
h2
�24
h
610
x2�
18x
8
16.(
3a�
b)(2
a�
b)17
.(4g
�3h
)(2g
�3h
)18
.(4x
�y)
(4x
�y)
6a2
�5a
b
b2
8g2
18
gh
9h
216
x2
8xy
y
2
19.(
m�
5)(m
2�
4m�
8)20
.(t
�3)
(t2
�4t
�7)
m3
9m
2
12m
�40
t3
7t2
19
t
21
21.(
2h�
3)(2
h2
�3h
�4)
22.(
3d�
3)(2
d2
�5d
�2)
4h3
12
h2
17
h
126d
3
21d
2
9d�
6
23.(
3q�
2)(9
q2�
12q
�4)
24.(
3r�
2)(9
r2�
6r�
4)27
q3
�18
q2
�12
q
827
r3
36r2
24
r
8
25.(
3c2
�2c
�1)
(2c2
�c
�9)
26.(
2�2
��
�3)
(4�2
�2�
�2)
6c4
7c
3
27c2
17
c�
98�
4
8�3
10
�2
4��
6
27.(
2x2
�2x
�3)
(2x2
�4x
�3)
28.(
3y2
�2y
�2)
(3y2
�4y
�5)
4x4
�12
x3
8x
2
6x�
99y
4�
6y3
�17
y2
�18
y�
10
GEO
MET
RYW
rite
an
exp
ress
ion
to
rep
rese
nt
the
area
of
each
fig
ure
.
29.
4x2
�2x
�2
un
its2
30.
4x2
3x
�1
un
its2
31.N
UM
BER
TH
EORY
Let
xbe
an
eve
n i
nte
ger.
Wh
at i
s th
e pr
odu
ct o
f th
e n
ext
two
con
secu
tive
eve
n i
nte
gers
?x2
6x
8
32.G
EOM
ETRY
Th
e vo
lum
e of
a r
ecta
ngu
lar
pyra
mid
is
one
thir
d th
e pr
odu
ct o
f th
e ar
eaof
its
bas
e an
d it
s h
eigh
t.F
ind
an e
xpre
ssio
n f
or t
he
volu
me
of a
rec
tan
gula
r py
ram
idw
hos
e ba
se h
as a
n a
rea
of 3
x2�
12x
�9
squ
are
feet
an
d w
hos
e h
eigh
t is
x�
3 fe
et.
x3
7x2
15
x
9 fe
et3
3x
2
5x �
4
x
1
4x
2
2x �
2
Pra
ctic
e (
Ave
rag
e)
Mu
ltip
lyin
g P
oly
no
mia
ls
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-7
8-7
Answers (Lesson 8-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csM
ult
iply
ing
Po
lyn
om
ials
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-7
8-7
©G
lenc
oe/M
cGra
w-H
ill49
5G
lenc
oe A
lgeb
ra 1
Lesson 8-7
Pre-
Act
ivit
yH
ow i
s m
ult
iply
ing
bin
omia
ls s
imil
ar t
o m
ult
iply
ing
two-
dig
itn
um
ber
s?
Rea
d th
e in
trod
uct
ion
to
Les
son
8-7
at
the
top
of p
age
452
in y
our
text
book
.
In y
our
own
wor
ds,e
xpla
in h
ow t
he
dist
ribu
tive
pro
pert
y is
use
d tw
ice
tom
ult
iply
tw
o-di
git
nu
mbe
rs.
Th
e o
nes
of
the
firs
t fa
cto
r ar
e m
ult
iplie
d b
y th
e te
ns
and
th
eo
nes
of
the
oth
er f
acto
r.T
hen
th
e te
ns
of
the
firs
t fa
cto
r ar
em
ult
iplie
d b
y th
e te
ns
and
on
es o
f th
e o
ther
fac
tor.
Rea
din
g t
he
Less
on
1.H
ow i
s m
ult
iply
ing
bin
omia
ls s
imil
ar t
o m
ult
iply
ing
two-
digi
t n
um
bers
?
Bin
om
ials
hav
e tw
o t
erm
s an
d e
ach
ter
m o
f o
ne
bin
om
ial i
s m
ult
iplie
d b
yea
ch t
erm
of
the
oth
er b
ino
mia
l.
2.C
ompl
ete
the
tabl
e u
sin
g th
e F
OIL
met
hod
.
Pro
du
ct o
f
Pro
du
ct o
f
Pro
du
ct o
f
Pro
du
ct o
f F
irst
Ter
ms
Ou
ter T
erm
sIn
ner
Ter
ms
Las
t Ter
ms
(x�
5)(x
�3)
�(x
)(x)
�(x
)(�
3)�
(5)(
x)�
(5)(
�3)
�x2
��
3x�
5x�
�15
�x2
�2x
�15
(3y
�6)
(y�
2)�
(3y)
(y)
�(3
y)(�
2)�
(6)(
y)�
(6)(
�2)
�3y
2�
�6y
�6y
��
12
�3y
2�
12
Hel
pin
g Y
ou
Rem
emb
er
3.T
hin
k of
a m
eth
od f
or r
emem
beri
ng
all
the
prod
uct
com
bin
atio
ns
use
d in
th
e F
OIL
met
hod
for
mu
ltip
lyin
g tw
o bi
nom
ials
.Des
crib
e yo
ur
met
hod
usi
ng
wor
ds o
r a
diag
ram
.S
amp
le a
nsw
er:
Imag
ine
that
th
e tw
o b
ino
mia
ls a
re w
ritt
en o
n t
he
flo
or.
Fo
r F
OIL
,th
ink
of
all t
he
po
ssib
le w
ays
you
co
uld
hav
e yo
ur
left
fo
ot
on
a te
rm o
f th
e fi
rst
bin
om
ial a
nd
yo
ur
rig
ht
foo
t o
n a
ter
m o
f th
e se
con
db
ino
mia
l.Yo
ur
feet
co
uld
be
on
th
e fi
rst
term
s,th
e o
ute
r te
rms,
the
inn
erte
rms,
or
the
last
ter
ms.
©G
lenc
oe/M
cGra
w-H
ill49
6G
lenc
oe A
lgeb
ra 1
Pas
cal’s
Tri
ang
leT
his
arr
ange
men
t of
nu
mb
ers
is c
alle
d P
asca
l’s T
rian
gle.
It w
as f
irst
pu
bli
shed
in
166
5,b
ut
was
kn
own
hu
nd
red
s of
yea
rs e
arli
er.
1.E
ach
nu
mbe
r in
th
e tr
ian
gle
is f
oun
d by
add
ing
two
nu
mbe
rs.
Wh
at t
wo
nu
mbe
rs w
ere
adde
d to
get
th
e 6
in t
he
5th
row
?
3 an
d 3
2.D
escr
ibe
how
to
crea
te t
he
6th
row
of
Pas
cal’s
Tri
angl
e.
Th
e fi
rst
and
last
nu
mb
ers
are
1.E
valu
ate
1
4,4
6,
6
4,an
d 4
1
to f
ind
th
e o
ther
nu
mb
ers.
3.W
rite
th
e n
um
bers
for
row
s 6
thro
ugh
10
of t
he
tria
ngl
e.
Row
6:
15
1010
51
Row
7:
16
1520
156
1R
ow 8
:1
721
3535
217
1R
ow 9
:1
828
5670
5628
81
Row
10:
19
3684
126
126
8436
91
Mu
ltip
ly t
o fi
nd
th
e ex
pan
ded
for
m o
f ea
ch p
rod
uct
.
4.(a
�b)
2a2
2a
b
b2
5.(a
�b)
3a3
3a
2 b
3ab
2
b3
6.(a
�b)
4a4
4a
3 b
6a2 b
2
4ab
3
b4
Now
com
par
e th
e co
effi
cien
ts o
f th
e th
ree
pro
du
cts
in E
xerc
ises
4–6
wit
h
Pas
cal’s
Tri
angl
e.
7.D
escr
ibe
the
rela
tion
ship
bet
wee
n t
he
expa
nde
d fo
rm o
f (a
�b)
nan
d P
asca
l’s T
rian
gle.
Th
e co
effi
cien
ts o
f th
e ex
pan
ded
fo
rm a
re f
ou
nd
in r
ow
n
1 o
f P
asca
l’sTr
ian
gle
.
8.U
se P
asca
l’s T
rian
gle
to w
rite
th
e ex
pan
ded
form
of
(a�
b)6 .
a6
6a5 b
15
a4b
2
20a3
b3
15
a2b
4
6ab
5
b6
11
11
21
13
31
14
64
1
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-7
8-7
Answers (Lesson 8-7)
© Glencoe/McGraw-Hill A23 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Sp
ecia
l Pro
du
cts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-8
8-8
©G
lenc
oe/M
cGra
w-H
ill49
7G
lenc
oe A
lgeb
ra 1
Lesson 8-8
Squ
ares
of
Sum
s an
d D
iffe
ren
ces
Som
e pa
irs
of b
inom
ials
hav
e pr
odu
cts
that
foll
ow s
peci
fic
patt
ern
s.O
ne
such
pat
tern
is
call
ed t
he
squ
are
of a
su
m.A
not
her
is
call
ed t
he
squ
are
of a
dif
fere
nce
.
Sq
uar
e o
f a
sum
(a�
b)2
�(a
�b)
(a�
b) �
a2
�2a
b�
b2
Sq
uar
e o
f a
dif
fere
nce
(a�
b)2
�(a
�b)
(a�
b) �
a2
�2a
b�
b2
Fin
d (
3a
4)(3
a
4).
Use
th
e sq
uar
e of
a s
um
pat
tern
,wit
h a
�3a
and
b�
4.
(3a
�4)
(3a
�4)
�(3
a)2
�2(
3a)(
4) �
(4)2
�9a
2�
24a
�16
Th
e pr
odu
ct i
s 9a
2�
24a
�16
.
Fin
d (
2z�
9)(2
z�
9).
Use
th
e sq
uar
e of
a d
iffe
ren
ce p
atte
rn w
ith
a�
2zan
d b
�9.
(2z
�9)
(2z
�9)
�(2
z)2
�2(
2z)(
9) �
(9)(
9)�
4z2
�36
z�
81
Th
e pr
odu
ct i
s 4z
2�
36z
�81
.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
pro
du
ct.
1.(x
�6)
22.
(3p
�4)
23.
(4x
�5)
2
x2
�12
x
369p
2
24p
16
16x2
�40
x
25
4.(2
x�
1)2
5.(2
h�
3)2
6.(m
�5)
2
4x2
�4x
1
4h2
12
h
9m
2
10m
25
7.(c
�3)
28.
(3 �
p)2
9.(x
�5y
)2
c2
6c
9
9 �
6p
p2
x2�
10xy
25
y2
10.(
8y�
4)2
11.(
8 �
x)2
12.(
3a�
2b)2
64y
2
64y
16
64
16x
x2
9a2
�12
ab
4b2
13.(
2x�
8)2
14.(
x2�
1)2
15.(
m2
�2)
2
4x2
�32
x
64x
4
2x2
1
m4
�4m
2
4
16.(
x3�
1)2
17.(
2h2
�k2
)218
. �x
�3 �2
x6
�2x
3 1
4h4
�4h
2 k2
k
4x2
x
9
19.(
x�
4y2 )
220
.(2p
�4q
)221
. �x
�2 �2
x2�
8xy
2
16y
44p
2
16p
q
16q
2x2
�x
4
8 � 34 � 92 � 3
3 � 21 � 161 � 4
©G
lenc
oe/M
cGra
w-H
ill49
8G
lenc
oe A
lgeb
ra 1
Pro
du
ct o
f a
Sum
an
d a
Dif
fere
nce
Th
ere
is a
lso
a pa
tter
n f
or t
he
prod
uct
of
asu
m a
nd
a di
ffer
ence
of
the
sam
e tw
o te
rms,
(a�
b)(a
�b)
.Th
e pr
odu
ct i
s ca
lled
th
ed
iffe
ren
ce o
f sq
uar
es.
Pro
du
ct o
f a
Su
m a
nd
a D
iffe
ren
ce(a
�b)
(a�
b) �
a2�
b2
Fin
d (
5x
3y)(
5x�
3y).
(a�
b)(a
�b)
�a2
�b2
Pro
duct
of
a S
um a
nd a
Diff
eren
ce
(5x
�3y
)(5x
�3y
) �
(5x)
2�
(3y)
2a
�5x
and
b�
3y
�25
x2�
9y2
Sim
plify
.
Th
e pr
odu
ct i
s 25
x2�
9y2 .
Fin
d e
ach
pro
du
ct.
1.(x
�4)
(x�
4)2.
(p�
2)(p
�2)
3.(4
x�
5)(4
x�
5)
x2�
16p
2�
416
x2�
25
4.(2
x�
1)(2
x�
1)5.
(h�
7)(h
�7)
6.(m
�5)
(m�
5)
4x2
�1
h2
�49
m2
�25
7.(2
c�
3)(2
c�
3)8.
(3 �
5q)(
3 �
5q)
9.(x
�y)
(x�
y)
4c2
�9
9 �
25q
2x2
�y2
10.(
y�
4x)(
y�
4x)
11.(
8 �
4x)(
8 �
4x)
12.(
3a�
2b)(
3a�
2b)
y2�
16x2
64 �
16x2
9a2
�4b
2
13.(
3y�
8)(3
y�
8)14
.(x2
�1)
(x2
�1)
15.(
m2
�5)
(m2
�5)
9y2
�64
x4
�1
m4
�25
16.(
x3�
2)(x
3�
2)17
.(h
2�
k2)(
h2
�k2
)18
. �x
�2 ��
x�
2 �x
6�
4h
4�
k4
x2�
4
19.(
3x�
2y2 )
(3x
�2y
2 )20
.(2p
�5s
)(2p
�5s
)21
. �x
�2y
��x
�2y
�9x
2�
4y4
4p2
�25
s2x2
�4y
216 � 9
4 � 34 � 31 � 16
1 � 41 � 4
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Sp
ecia
l Pro
du
cts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-8
8-8
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 8-8)
© Glencoe/McGraw-Hill A24 Glencoe Algebra 1
Skil
ls P
ract
ice
Sp
ecia
l Pro
du
cts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-8
8-8
©G
lenc
oe/M
cGra
w-H
ill49
9G
lenc
oe A
lgeb
ra 1
Lesson 8-8
Fin
d e
ach
pro
du
ct.
1.(n
�3)
22.
(x�
4)(x
�4)
n2
6n
9
x2
8x
16
3.(y
�7)
24.
(t�
3)(t
�3)
y2
�14
y
49t2
�6t
9
5.(b
�1)
(b�
1)6.
(a�
5)(a
�5)
b2
�1
a2�
25
7.(p
�4)
28.
(z�
3)(z
�3)
p2
�8p
16
z2�
9
9.(�
�2)
(��
2)10
.(r
�1)
(r�
1)
�2
4�
4r2
�2r
1
11.(
3g�
2)(3
g�
2)12
.(2m
�3)
(2m
�3)
9g2
�4
4m2
�9
13.(
6 �
u)2
14.(
r�
s)2
36
12u
u
2r2
2r
s
s2
15.(
3q�
1)(3
q�
1)16
.(c
�e)
2
9q2
�1
c2�
2ce
e
2
17.(
2k�
2)2
18.(
w�
3h)2
4k2
�8k
4
w2
6w
h
9h2
19.(
3p�
4)(3
p�
4)20
.(t
�2u
)2
9p2
� 1
6t2
4t
u
4u2
21.(
x�
4y)2
22.(
3b�
7)(3
b�
7)
x2�
8xy
16
y2
9b2
�49
23.(
3y�
3g)(
3y�
3g)
24.(
s2�
r2)2
9y2
�9g
2s4
2s
2 r2
r4
25.(
2k�
m2 )
226
.(3u
2�
n)2
4k2
4k
m2
m
49u
4�
6u2 n
n
2
27.G
EOM
ETRY
Th
e le
ngt
h o
f a
rect
angl
e is
th
e su
m o
f tw
o w
hol
e n
um
bers
.Th
e w
idth
of
the
rect
angl
e is
th
e di
ffer
ence
of
the
sam
e tw
o w
hol
e n
um
bers
.Usi
ng
thes
e fa
cts,
wri
te a
verb
al e
xpre
ssio
n f
or t
he
area
of
the
rect
angl
e.T
he
area
is t
he
squ
are
of
the
larg
er n
um
ber
min
us
the
squ
are
of
the
smal
ler
nu
mb
er.
©G
lenc
oe/M
cGra
w-H
ill50
0G
lenc
oe A
lgeb
ra 1
Fin
d e
ach
pro
du
ct.
1.(n
�9)
22.
(q�
8)2
3.(�
�10
)2
n2
18
n
81q
2
16q
64
�2�
20�
10
0
4.(r
�11
)25.
(p�
7)2
6.(b
�6)
(b�
6)r2
�22
r
121
p2
14
p
49b
2�
36
7.(z
�13
)(z
�13
)8.
(4e
�2)
29.
(5w
�4)
2
z2�
169
16e
2
16e
4
25w
2�
40w
16
10.(
6h�
1)2
11.(
3s�
4)2
12.(
7v�
2)2
36h
2�
12h
1
9s2
24
s
1649
v2
�28
v
4
13.(
7k�
3)(7
k�
3)14
.(4d
�7)
(4d
�7)
15.(
3g�
9h)(
3g�
9h)
49k
2�
916
d2
�49
9g2
�81
h2
16.(
4q�
5t)(
4q�
5t)
17.(
a�
6u)2
18.(
5r�
s)2
16q
2�
25t2
a2
12
au
36u
225
r2
10rs
s2
19.(
6c�
m)2
20.(
k�
6y)2
21.(
u�
7p)2
36c
2�
12cm
m
2k2
�12
ky
36y
2u
2�
14u
p
49p
2
22.(
4b�
7v)2
23.(
6n�
4p)2
24.(
5q�
6s)2
16b
2�
56bv
49
v2
36n
2
48n
p
16p
225
q2
60
qs
36
s2
25.(
6a�
7b)(
6a�
7b)
26.(
8h�
3d)(
8h�
3d)
27.(
9x�
2y2 )
2
36a2
�49
b2
64h
2�
9d2
81x2
36
xy2
4y
4
28.(
3p3
�2m
)229
.(5a
2�
2b)2
30.(
4m3
�2t
)2
9p6
12
p3 m
4m
225
a4�
20a2
b
4b2
16m
6�
16m
3 t
4t2
31.(
6e3
�c)
232
.(2b
2�
g)(2
b2�
g)33
.(2v
2�
3e2 )
(2v2
�3e
2 )36
e6�
12e
3 c
c2
4b4
�g
24v
4
12v2
e2
9e4
34.G
EOM
ETRY
Jan
elle
wan
ts t
o en
larg
e a
squ
are
grap
h t
hat
sh
e h
as m
ade
so t
hat
a s
ide
of t
he
new
gra
ph w
ill
be 1
in
ch m
ore
than
tw
ice
the
orig
inal
sid
e s.
Wh
at t
rin
omia
lre
pres
ents
th
e ar
ea o
f th
e en
larg
ed g
raph
?4s
2
4s
1
GEN
ETIC
SF
or E
xerc
ises
35
and
36,
use
th
e fo
llow
ing
info
rmat
ion
.In
a g
uin
ea p
ig,p
ure
bla
ck h
air
colo
rin
g B
is d
omin
ant
over
pu
re w
hit
e co
lori
ng
b.S
upp
ose
two
hyb
rid
Bb
guin
ea p
igs,
wit
h b
lack
hai
r co
lori
ng,
are
bred
.
35.F
ind
an e
xpre
ssio
n f
or t
he
gen
etic
mak
e-u
p of
th
e gu
inea
pig
off
spri
ng.
0.25
BB
0.
50B
b
0.25
bb
36.W
hat
is
the
prob
abil
ity
that
tw
o h
ybri
d gu
inea
pig
s w
ith
bla
ck h
air
colo
rin
g w
ill
prod
uce
a gu
inea
pig
wit
h w
hit
e h
air
colo
rin
g?25
%
Pra
ctic
e (
Ave
rag
e)
Sp
ecia
l Pro
du
cts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-8
8-8
Answers (Lesson 8-8)
© Glencoe/McGraw-Hill A25 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csS
pec
ial P
rod
uct
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-8
8-8
©G
lenc
oe/M
cGra
w-H
ill50
1G
lenc
oe A
lgeb
ra 1
Lesson 8-8
Pre-
Act
ivit
yW
hen
is
the
pro
du
ct o
f tw
o b
inom
ials
als
o a
bin
omia
l?
Rea
d th
e in
trod
uct
ion
to
Les
son
8-8
at
the
top
of p
age
458
in y
our
text
ook.
Wh
at i
s a
mea
nt
by t
he
term
tri
nom
ial
prod
uct
?
a th
ree-
term
po
lyn
om
ial a
nsw
er w
hen
mu
ltip
lyin
g p
oly
no
mia
ls
Rea
din
g t
he
Less
on
1.R
efer
to
the
Key
Con
cept
s bo
xes
on p
ages
458
,459
,an
d 46
0.
a.W
hen
mu
ltip
lyin
g tw
o bi
nom
ials
,th
ere
are
thre
e sp
ecia
l pr
odu
cts.
Wh
at a
re t
he
thre
esp
ecia
l pr
odu
cts
that
may
res
ult
wh
en m
ult
iply
ing
two
bin
omia
ls?
squ
are
of
a su
m,s
qu
are
of
a d
iffe
ren
ce,p
rod
uct
of
a su
m a
nd
ad
iffe
ren
ce
b.
Exp
lain
wh
at i
s m
ean
t by
th
e n
ame
of e
ach
spe
cial
pro
duct
.
squ
are
of
a su
m:
squ
arin
g t
he
sum
of
two
mo
no
mia
ls;
squ
are
of
ad
iffe
ren
ce:
squ
arin
g t
he
dif
fere
nce
of
two
mo
no
mia
ls;
pro
du
ct o
f a
sum
an
d a
dif
fere
nce
:th
e p
rod
uct
of
the
sum
an
d t
he
dif
fere
nce
of
the
sam
e tw
o t
erm
sc.
Use
th
e ex
ampl
es i
n t
he
Key
Con
cept
s bo
xes
to c
ompl
ete
the
tabl
e.
Sym
bo
lsP
rod
uct
Exa
mp
leP
rod
uct
Sq
uar
e o
f a
Su
m(a
�b
)2a
2�
2ab
�b
2(x
�7)
2x
2�
14x
�49
Sq
uar
e o
f a
Dif
fere
nce
(a�
b)2
a2
�2a
b�
b2
(x�
4)2
x2
�8x
�16
Pro
du
ct o
f a
Su
m
and
a D
iffe
ren
ce(a
�b
)(a
�b
)a
2�
b2
(x�
9)(x
�9)
x2
�81
2.W
hat
is
anot
her
ph
rase
th
at d
escr
ibes
th
e pr
odu
ct o
f th
e su
m a
nd
diff
eren
ce o
f tw
o te
rms?
dif
fere
nce
of
squ
ares
Hel
pin
g Y
ou
Rem
emb
er
3.E
xpla
in h
ow F
OIL
can
hel
p yo
u r
emem
ber
how
man
y te
rms
are
in t
he
spec
ial
prod
uct
sst
udi
ed i
n t
his
les
son
.F
or
the
squ
are
of
a su
m a
nd
th
e sq
uar
e o
f a
dif
fere
nce
,th
e in
ner
an
d o
ute
r p
rod
uct
s ar
e eq
ual
,so
th
ere
are
are
on
lyth
ree
term
s.F
or
the
pro
du
ct o
f th
e su
m a
nd
dif
fere
nce
of
two
ter
ms,
two
of
the
pro
du
cts
for
FO
IL a
re o
pp
osi
tes.
Th
at m
ean
s th
at t
he
fin
al p
rod
uct
has
on
ly t
wo
ter
ms.
©G
lenc
oe/M
cGra
w-H
ill50
2G
lenc
oe A
lgeb
ra 1
Su
ms
and
Diff
eren
ces
of
Cu
bes
R
ecal
l th
e fo
rmu
las
for
fin
din
g so
me
spec
ial
prod
uct
s:
Per
fect
-squ
are
trin
omia
ls:
(a�
b)2
�a2
�2a
b�
b2or
(a
�b)
2�
a2�
2ab
�b2
Dif
fere
nce
of
two
squ
ares
:(a
�b)
(a�
b) �
a2�
b2
A p
atte
rn a
lso
exis
ts f
or f
indi
ng
the
cube
of
a su
m (
a�
b)3 .
1.F
ind
the
prod
uct
of
(a�
b)(a
�b)
(a�
b).
a3
�3a
2 b�
3ab
2�
b3
2.U
se t
he
patt
ern
fro
m E
xerc
ise
1 to
eva
luat
e (x
�2)
3 .
x3
�6x
2�
12x
�8
3.B
ased
on
you
r an
swer
to
Exe
rcis
e 1,
pred
ict
the
patt
ern
for
th
e cu
be o
f a
diff
eren
ce (
a�
b)3 .
a3
�3a
2 b�
3ab
2�
b3
4.F
ind
the
prod
uct
of
(a�
b)(a
�b)
(a�
b) a
nd
com
pare
it
to y
our
answ
er f
or E
xerc
ise
3.
a3
�3a
2 b�
3ab
2�
b3
5.U
se t
he
patt
ern
fro
m E
xerc
ise
4 to
eva
luat
e (x
�4)
3 .
x3
�12
x2
�48
x�
64
Fin
d e
ach
pro
du
ct.
6.(x
�6)
37.
(x�
10)3
x3
�18
x2
�10
8x�
216
x3
�30
x2
�30
0x�
1000
8.(3
x�
y)3
9.(2
x�
y)3
27x
3�
27x
2 y�
9xy
2�
y3
8x3
�12
x2 y
�6x
y2
�y
3
10.(
4x�
3y)3
11.(
5x�
2)3
64x
3�
144x
2 y�
108x
y2
�27
y3
125x
3�
150x
2�
60x
�8
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
8-8
8-8
Answers (Lesson 8-8)
© Glencoe/McGraw-Hill A26 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. A
C
C
B
A
D
D
C
D
A
C
39n � 1
B
B
D
D
C
A
A
B
D
C
A
C
D
C
B
A
A
C
B
D
D
C
C
A
B
Chapter 8 Assessment Answer Key Form 1 Form 2APage 503 Page 504 Page 505
(continued on the next page)
© Glencoe/McGraw-Hill A27 Glencoe Algebra 1
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 37n � 1
C
A
D
B
A
A
D
D
B
C
A
D
C
D
B
B
D
C
B
B
7�2x � 2
C
A
C
C
A
B
C
A
D
An
swer
s
Chapter 8 Assessment Answer Key Form 2A (continued) Form 2BPage 506 Page 507 Page 508
An
swer
s
© Glencoe/McGraw-Hill A28 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B: 21 terms
length is 20 ft;width is 12 ft
6
2�25
�
16n2 � 8n � 1
49a2 � 9b2
25c2 � 40c � 16
6s3 � 14s2 � 22s � 30
8x4 � 2y4
10h3k3 � 5h2k5 �20h3k4
�x2 � y
19m2 � 2mn � 6n2
�4n2 � 6ny � 13y2
�x5y � 3x3y3 � xy � 4
6
about 1.09 � 102 or 109times greater
1.0 � 105; 100,000
127,000
4.98 � 10�4
�xy5�
�4sr7
4�
p3q
8a3n6 � 4a18n6
w15y12
�18m4n7
3y8
Chapter 8 Assessment Answer Key Form 2CPage 509 Page 510
© Glencoe/McGraw-Hill A29 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B: 11 terms
length is 10 ft;width is 5 ft
–2
13
4c2 � 4c � 1
4k2 � 25r2
25y2 � 60y � 36
6n3 � n2 � 10n � 3
9r4 � 25s4
6x4y2 � 15x3y3 �24x4y4
a3 � 3b
8y2 � 4y � 9
4m2 � 6m � 1
x3 � 3x2y � xy2 � 3y3
5
2 � 107; 20,000,000
about 1.43 � 1010
or 14,300,000,000 in.
0.00743
1.2556 � 104
3r5s
�2db
7
5�
��m3
2�
10a4b8
w9z21
�6a3b8
5x7
An
swer
s
Chapter 8 Assessment Answer Key Form 2DPage 511 Page 512
An
swer
s
© Glencoe/McGraw-Hill A30 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:�1�2�3�4 0 1 2 43
length is 16 cm;width is 12 cm
5
2a2 � 7a � 5
4
(9x2 � 6x � 1) ft2
25r4 � 9s4
8x3 � 2x2y � 19xy2 � 5y3
�13
�m2 � �161�m � 2
8y2 � 20y � 28
�n3 � 25n2 � 12n � 21
3x2 � x � 5y
10u2v � 7uv � 6uv2
10w2 � 3w � 4
6
7x6y3 � 4x5y2 � 2xy � 6
9.0 � 10�6; 0.000009
5.832 � 10�4;0.0005832
1.96783 � 105
��125
1a6
11b�
�m12
x8
12�
��6cd4
3�
45x�2
25r4s14
�1861�h12
3a7b10
An
swer
s
Chapter 8 Assessment Answer Key Form 3Page 513 Page 514
Chapter 8 Assessment Answer KeyPage 515, Open-Ended Assessment
Scoring Rubric
© Glencoe/McGraw-Hill A31 Glencoe Algebra 1
Score General Description Specific Criteria
• Shows thorough understanding of the concepts ofmultiplying and dividing monomials, using scientificnotation, the degree of a polynomial, and adding,subtracting, and multiplying polynomials.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of multiplyingand dividing monomials, using scientific notation, thedegree of a polynomial, and adding, subtracting, andmultiplying polynomials.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts ofmultiplying and dividing monomials, using scientificnotation, the degree of a polynomial, and adding,subtracting, and multiplying polynomials.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs are mostly accurate.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work is shown to substantiate
the final computation.• Graphs may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the concepts ofmultiplying and dividing monomials, using scientificnotation, the degree of a polynomial, and adding,subtracting, and multiplying polynomials.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer may be given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
An
swer
s
© Glencoe/McGraw-Hill A32 Glencoe Algebra 1
Chapter 8 Assessment Answer Key Page 515, Open-Ended Assessment
Sample Answers
1a. Students should recognize that the v terms were not subtractedcorrectly. Since �5v � ( � v)� �5v � v � �6v, the right side of theequation should be 3u � 6v.
1b. Students should recognize that theProduct of a Power property was notused correctly to multiply x2y(3x3). Theright side of the equation should be3x5y � 4x2y.
1c. Students should recognize that thepattern for the Square of a Sum was notused correctly. The middle term2(3a)(5b) was omitted. Since(3a � 5b)2 � (3a)2 � 2(3a)(5b) � (5b)2,the right side of the equation should be9a2 � 30ab � 25b2.
2a. The number 23.4 � 108 is not inscientific notation. A number inscientific notation is of the form a � 10b where 1 � a � 10. The numberneeds to be adjusted to fit the form ofscientific notation.23.4 � 108 � 2.34 � 10 � 108
� 2.34 � 109
2b. Using scientific notation for division ofvery large and small numbers results inthe division of two numbers that arebetween one and ten. The correctdecimal place is found by using theQuotient of Powers property on twopowers of ten. Thus, 22,100,000 �0.00000013 � 2.21 � 107�1.3 � 10�7
� 12..321
�
�
101
�
07
7 � 21.2.31
� 1100�
7
7 � 1.7 � 1014
3a. Sample Answer: The binomial x � 1 hasdegree 1.
3b. Sample Answer: The trinomialx2 � x � 1 has degree 2, yet themonomial x3 has degree 3.
4a. �24aa�3
2�4� (2a5)4 � 16a20
4b. �24aa�3
2�4� (
(24aa�
3
2))4
4 � 21566aa�
1
8
2 � 16a20
4c. Sample answer: When simplifyingmonomials, the order of applying theQuotient of Powers property and Powerof a Quotient property does not matter.
5a.
3x2 � 7xy � 2y2
The length of the rectangular region is3x � y. The width of the region isx � 2y.The rectangular area is made upof 3 x2-areas, 7 xy-areas, and 2 y2-areas.When added together the area of therectangular region is exactly equal tothe product of the two binomials.
3x � y
x � 2y
x
x
x x y
yy
In addition to the scoring rubric found on page A31, the following sample answers may be used as guidance in evaluating open-ended assessment items.
© Glencoe/McGraw-Hill A33 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. the sum of theexponents of all thevariables
12. the greatest degreeof any term
13. a number written asa product of a factorgreater than orequal to 1 and lessthan 10 and a powerof 10
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Quiz (Lessons 8–3 and 8–4)
Page 517
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.
2.
3.
4.
5.
Quiz (Lesson 8–7)
Page 518
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.(4a3 � 12a2 � 4a � 12)
units3
(4a2 � 4) units2
a2 � 9b2
81x2 � 49
m4 � 4m2n � 4n2
4x2 � 36y2
a2 � 18a � 81
16h2 � 24h � 9
2c3 � 11c2 � 22c � 15
4m2 � 7m � 2
2
�3c3 � 74c2 � 4c
6x3y � 15x2y2 � 21xy3
3a � 5b
3x2 � 3x � 4
�3 � 4x � x2
5x3y � x2y3 � 3xy4 � y4
�3x3 � 4x2 � 2x � 12
4
2
2.87 � 1010;28,700,000,000
1.6 � 10�7; 0.00000016
0.0064871
6.1 � 10�6
5.76 � 104
C
�nr2
9�
y5
66 or 46,65627y4w8
64c8d2
�125x12y6
�12m3n7
x20
2r8
h
d
b
j
a
i
f
g
c
e
Chapter 8 Assessment Answer Key Vocabulary Test/Review Quiz (Lessons 8–1 and 8–2) Quiz (Lessons 8–5 and 8–6)
Page 516 Page 517 Page 518
An
swer
s
© Glencoe/McGraw-Hill A34 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14. 9x2 � 12x � 4
�13
�a2 � a � �35
�
1.38 � 109; 1,380,000,000
�3xy3
2�
elimination (x); (1, –1)
y
xO
x � y � 4
y � x
(2, 2)
one solution; (2, 2)
8x � 12y � 62
�y � y � 3�23
��{u � u � 3}
y � 4x � 9
$122.50 per yr.
f(x) � 2x � 2
c � b � �b1
�
10
8x4 � 2a2x3 �3a4x2 � 8x
4x3 � 2x2 � 3x � 6
4
�5m6
7y3r5�
�5x
29y�
7.553 � 10�4; 0.0007553
2.34 � 102; 234
A
D
C
A
A
A
B
Chapter 8 Assessment Answer Key Mid-Chapter Test Cumulative ReviewPage 519 Page 520
© Glencoe/McGraw-Hill A35 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 12.
13. 14.
15.
16.
17. DCBA
DCBA
DCBA
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
. 0 5 7
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
5
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
3 . 5 0
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
1 0 8
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
Chapter 8 Assessment Answer KeyStandardized Test Practice
Page 521 Page 522
An
swer
s