algebraic expressions 2x + 3y - 7
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Algebraic Expressions 2x + 3y - 7 TermsTRANSCRIPT
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Algebraic Expressions
2x + 3y - 7What are the Terms?
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Algebraic Expressions
2x + 3y - 7
Terms
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Algebraic Expressions
2x + 3y - 7What are the variables?
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Algebraic Expressions
2x + 3y - 7
Variables
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Algebraic Expressions
2x + 3y - 7What are the coefficients?
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Algebraic Expressions
2x + 3y - 7
Coefficients
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Algebraic Expressions
2x + 3y - 7What is the constant?
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Algebraic Expressions
2x + 3y - 7Constant
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Algebraic ExpressionsPolynomial:monomial → x, 2xy, 4, 3x²y, … single termbinomial → x+1, 2xy+x, 3x²y+4, …two termstrinomial → 2x+3y+7, 3x²y+xy+4x, …three termspolynomial → …four or more terms
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What is the area of a rectangle?
Length times WidthIf the length is 3 meters and the width is 2
meters, what is the area?A = L x W
A = 3 x 2 = 6 meters2
A, L and W are the variables. It is any letter that represents an unknown number.
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An algebraic expression contains:
1) one or more numbers or variables, and
2) one or more arithmetic operations. Examples:
x - 33 • 2n4 1m
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In expressions, there are many different ways to write multiplication.
1) ab 2) a • b 3) a(b) or (a)b 4) (a)(b) 5) a x b
We are not going to use the multiplication symbol any more. Why?
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Division, on the other hand, is written as:
1)
2) x ÷ 3
x3
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Here are some phrases you may have see throughout the year. The terms with * are
ones that are often used.Addition Subtraction Multiplication Divisionsum* difference* product* quotient*increase decrease times dividedplus minus multiplied ratioadd subtractmore than less thantotal
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Write an algebraic expression for
1) m increased by 5.m + 5
2) 7 times the product of x and t.7xt or 7(x)(t) or 7 • x • t
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3) 11 less than 4 times a number.
4n - 11
4) two more than 6 times a number.
6n + 2
5) the quotient of a number and 12.
12x
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Which of the following expressions represents 7 times a number decreased by 13?
1. 7x + 132. 7x - 133. 13 - 7x4. 13 + 7x
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Which one of the following expressions represents 28 less than three times a number?
1. 28 - 3x2. 3x - 283. 28 + 3x4. 3x + 28
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Write a verbal expression for:
1) 8 + a.
The ratio of m to rDo you have a different way of writing these?
The sum of 8 and a2)
mr
.
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Which of the following verbal expressions represents 2x + 9?
1. 9 increased by twice a number2. a number increased by nine3. twice a number decreased by 94. 9 less than twice a number
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Which of the following expressions represents the sum of 16 and five times a number?
1. 5x - 162. 16x + 53. 16 + 5x4. 16 - 5x
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Which of the following verbal expressions represents x2 + 2x?
1. the sum of a number squared and twice the number
2. the sum of a number and twice the number
3. twice a number less than the number squared
4. the sum of a number and twice the number squared
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Which of the following expressions represents four less than the cube of a number?
1. 4 – x3
2. 4 – 3x3. 3x – 44. x3 – 4
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Evaluate.21 222 2 • 2 = 423 2 • 2 • 2 = 82n7 We can’t evaluate because
we don’t know what n equals to!!
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Competition Problems
Evaluating Algebraic Expressions
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Evaluate the following algebraic expression using
m=7, n=8
n² - m
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Answer:
57
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Evaluate the following algebraic expression using
x=5, y=2
8(x-y)
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Answer:
24
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Evaluate the following algebraic expression using
x=7, y=2
yx ÷ 2
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Answer:
7
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Evaluate the following algebraic expression using
x=1, z=19
z + x³
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Answer:
20
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Evaluate the following algebraic expression using
m=3, p=10
15-(m+p)
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Answer:
2
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Evaluate the following algebraic expression using
a=9, b=4
b(a+b) + a
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Answer:
61
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Evaluate the following algebraic expression using
m=3, p=4
p²÷4-m
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Answer:
1
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Evaluate the following algebraic expression using
x=4, y=2
y(x-(9-4y))
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Answer:
6
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Evaluate the following algebraic expression using
x=9, y=1
x-(x-(x-y³))
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Answer:
8
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Evaluate the following algebraic expression using
h=9, j=8
j(h-9)³ +2
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Answer:
2
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Simplifying Algebraic Expressions
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REVIEW
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Vocabularytermcoefficientlike terms
Insert Lesson Title Here
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The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms.
4x – 3x + 2
Like terms Constant
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A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1.
1x2 + 3x
Coefficients
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In the expression 7x + 5, 7x and 5 are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by + and –.
7x + 5 – 3y2 + y + x3
term term term term
In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y.
Coefficient Variable
term
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Term
Coefficient
4a 23 3k2 x2 x
9 4.7t
4 23 3 1 1
9 4.7
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Like terms are terms with the same variable raised to the same power. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms.1
2
Like Terms
Unlike Terms
3x and 2x
5x2 and 2xThe exponentsare different.
3.2 and nOnly one term
contains avariable
6a and 6bThe variablesare different
w and w7 5 and 1.8
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Identify like terms in the list.
Additional Example 1: Identifying Like Terms
3t 5w2 7t 9v 4w2 8v
Look for like variables with like powers.
3t 5w2 7t 9v 4w2 8v
Like terms: 3t and 7t, 5w2 and 4w2, 9v and 8v
Use different shapes or colors to indicate sets of like terms.Helpful Hint
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Insert Lesson Title HereIdentify like terms in the list.
2x 4y3 8x 5z 5y3 8z
Look for like variables with like powers.
Like terms: 2x and 8x, 4y3 and 5y3 , 5z and 8z
2x 4y3 8x 5z 5y3 8z
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Insert Lesson Title Here
x
Combining like terms is like grouping similar objects.
+ =x
x
x
x x
x x x
x x x x
x x x x x
4x + 5x = 9x
To combine like terms that have variables, add orsubtract the coefficients.
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Using the Distributive Property can help you combine like terms. You can factor out the common factors to
simplify the expression.
7x2 – 4x2 = (7 – 4)x2
= (3)x2
= 3x2
Factor out x2 from both terms.
Perform operations in parenthesis.
Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.
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Simplify the expression by combining like terms.
72p – 25p
72p – 25p
47p
72p and 25p are like terms.
Subtract the coefficients.
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Simplify the expression by combining like terms.
A variable without a coefficient has a coefficient of 1.
Write 1 as .
Add the coefficients.
and are like terms.
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Simplify the expression by combining like terms.
0.5m + 2.5n
0.5m + 2.5n
0.5m + 2.5n
0.5m and 2.5n are not like terms.
Do not combine the terms.
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Simplify by combining like terms.
16p + 84p16p + 84p
100p
16p + 84p are like terms.
Add the coefficients.
–20t – 8.5t2
–20t – 8.5t2 20t and 8.5t2 are not like terms.
–20t – 8.5t2 Do not combine the terms.
3m2 + m3 3m2 and m3 are not like terms.3m2 + m3
Do not combine the terms.3m2 + m3
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Simplify 14x + 4(2 + x)
14x + 4(2) + 4(x) Distributive Property
Multiply.
Commutative Property
Associative Property
Combine like terms.
14x + 8 + 4x
(14x + 4x) + 8
14x + 4x + 8
18x + 8
14x + 4(2 + x)1.
2.
3.
4.
5.
6.
Procedure Justification
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6(x) – 6(4) + 9 Distributive Property
Multiply.
Combine like terms.
6x – 24 + 9
6x – 15
6(x – 4) + 91.
2.
3.
4.
Procedure Justification
Simplify 6(x – 4) + 9. Justify each step.
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–12x – 5x + x + 3a Commutative Property
Combine like terms.–16x + 3a
–12x – 5x + 3a + x1.
2.
3.
Procedure Justification
Simplify −12x – 5x + 3a + x. Justify each step.
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Simplify each expression.
165 +27 + 3 + 5
Write each product using the Distributive Property. Then simplify.
5($1.99)
6(13)
200
8
5($2) – 5($0.01) = $9.95
6(10) + 6(3) = 78
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Simplify each expression by combining like terms. Justify each step with an operation or property.
301x – x
24a + b2 + 3a + 2b2
300x
27a + 3b2
14c2 – 9c 14c2 – 9c
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Let’s work more problems…
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Simplify the following algebraic expression:
-3p + 6p
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Answer:
3p
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Simplify the following algebraic expression:
7x - x
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Answer:
6x
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Simplify the following algebraic expression:
-10v + 6v
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Answer:
-4v
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Simplify the following algebraic expression:
5n + 9n
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Answer:
14n
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Simplify the following algebraic expression:
b - 3 + 6 - 2b
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Answer:
-b + 3
![Page 78: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/78.jpg)
Simplify the following algebraic expression:
10x + 36 - 38x - 47
![Page 79: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/79.jpg)
Answer:
-28x - 11
![Page 80: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/80.jpg)
Simplify the following algebraic expression:
10x-w+4y-3x+36-38x-47+32x+2w-3y
![Page 81: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/81.jpg)
Answer:
w+x+y-11
![Page 82: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/82.jpg)
Simplify the following algebraic expression using the distributive property:
6(1 – 5m)
![Page 83: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/83.jpg)
Answer:
6 – 30m
![Page 84: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/84.jpg)
Simplify the following algebraic expression using the distributive property:
-2(1 – 5v)
![Page 85: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/85.jpg)
Answer:
-2 + 10v
![Page 86: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/86.jpg)
Simplify the following algebraic expression using the distributive property:
-3(7n + 1)
![Page 87: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/87.jpg)
Answer:
-21n - 3
![Page 88: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/88.jpg)
Simplify the following algebraic expression using the distributive property:
(x + 1) 14∙
![Page 89: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/89.jpg)
Answer:
14x + 14
![Page 90: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/90.jpg)
Simplify the following algebraic expression using the distributive property:
(3 - 7k) (-2)∙
![Page 91: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/91.jpg)
Answer:
-6 + 14k
![Page 92: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/92.jpg)
Simplify the following algebraic expression using the distributive property:
-20(8x + 20)
![Page 93: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/93.jpg)
Answer:
-160x - 400
![Page 94: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/94.jpg)
Simplify the following algebraic expression using the distributive property:
(7 + 19b) -15∙
![Page 95: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/95.jpg)
Answer:
-105 – 285b
![Page 96: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/96.jpg)
Variable Expressions
))()((
))()()()(()(
3
5
yyymeansy
xxxxxtionmultiplicaforsparentheseusemeansx
![Page 97: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/97.jpg)
Simplify:
(-a)²
![Page 98: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/98.jpg)
Answer:
a²
![Page 99: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/99.jpg)
Substitution and EvaluatingSTEPS
1. Write out the original problem.2. Show the substitution with parentheses.3. Work out the problem.
3;4: xxifSolveExample 3;4 xxifSolve
3)4( = 64
![Page 100: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/100.jpg)
Evaluate the variable expression when x = 1, y = 2, and w = -3
22 )()( yx
22 )()( yx
22 )2()1(
541
Step 1
Step 2
Step 3
2)( yx
2)( yx
2)2()1(
9)3( 2
Step 1
Step 2
Step 3
ywx
ywx
2)1)(3(
Step 1
Step 2
Step 3
3)1)(3(
![Page 101: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/101.jpg)
Contest Problem
![Page 102: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/102.jpg)
Are you ready?3, 2, 1…lets go!
![Page 103: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/103.jpg)
Evaluate the expression when a= -2
a² + 2a - 6
![Page 104: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/104.jpg)
Answer:
-6
![Page 105: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/105.jpg)
Evaluate the expression when x= -4 and t=2
x²(x-t)
![Page 106: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/106.jpg)
Answer:
-96
![Page 107: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/107.jpg)
Evaluate the expression when y= -3
(2y + 5)²
![Page 108: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/108.jpg)
Answer:
1
![Page 109: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/109.jpg)
MULTIPLICATION PROPERTIESPRODUCT OF POWERS
This property is used to combine 2 or more exponential expressions with the SAME base.
53 22 )222( )22222( 82 256
))(( 43 xx ))()(( xxx ))()()(( xxxx 7x
![Page 110: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/110.jpg)
MULTIPLICATION PROPERTIESPOWER OF PRODUCT
This property combines the first 2 multiplication properties to simplify exponential expressions.
2)56( )5()6( 22 9002536
3)5( xy ))()(5( 333 yx33125 yx
532 )4( xx 5323 ))(4( xx 5222 ))()(()64( xxxx
56 ))(64( xx 1164x
![Page 111: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/111.jpg)
Problems
Are you ready?3, 2, 1…lets go!
![Page 112: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/112.jpg)
Simplify. Your answer should contain only positive exponents.
2n⁴ · 5n ⁴
![Page 113: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/113.jpg)
Answer:
10n⁸
![Page 114: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/114.jpg)
Simplify. Your answer should contain only positive exponents.
6r · 5r²
![Page 115: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/115.jpg)
Answer:
30r³
![Page 116: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/116.jpg)
Simplify. Your answer should contain only positive exponents.
6x · 2x²
![Page 117: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/117.jpg)
Answer:
12x³
![Page 118: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/118.jpg)
Simplify. Your answer should contain only positive exponents.
6x² · 6x³y⁴
![Page 119: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/119.jpg)
Answer:
36x⁵y⁴
![Page 120: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/120.jpg)
Simplify. Your answer should contain only positive exponents.
10xy³ · 8x⁵y³
![Page 121: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/121.jpg)
Answer:
80x⁶y⁶
![Page 122: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/122.jpg)
MULTIPLICATION PROPERTIESPOWER TO A POWER
This property is used to write and exponential expression as a single power of the base.
32 )5( )5)(5)(5( 222 65
42 )(x ))()()(( 2222 xxxx 8x
![Page 123: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/123.jpg)
MULTIPLICATION PROPERTIESSUMMARY
PRODUCT OF POWERSbaba xxx
POWER TO A POWER baba xx
POWER OF PRODUCTaaa yxxy )(
ADD THE EXPONENTS
MULTIPLY THE EXPONENTS
![Page 124: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/124.jpg)
Problems
Are you ready?3, 2, 1…lets go!
![Page 125: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/125.jpg)
Simplify. Your answer should contain only positive exponents.
(a²)³
![Page 126: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/126.jpg)
Answer:
a⁶
![Page 127: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/127.jpg)
Simplify. Your answer should contain only positive exponents.
(3a²)³
![Page 128: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/128.jpg)
Answer:
27a⁶
![Page 129: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/129.jpg)
Simplify. Your answer should contain only positive exponents.
(x⁴y⁴)³
![Page 130: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/130.jpg)
Answer:
x¹²y¹²
![Page 131: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/131.jpg)
Simplify. Your answer should contain only positive exponents.
(2x⁴y⁴)³
![Page 132: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/132.jpg)
Answer:
8x¹²y¹²
![Page 133: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/133.jpg)
Simplify. Your answer should contain only positive exponents.
(4x⁴ x⁴)³∙
![Page 134: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/134.jpg)
Answer:
64x²⁴
![Page 135: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/135.jpg)
Simplify. Your answer should contain only positive exponents.
(4n⁴ n)²∙
![Page 136: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/136.jpg)
Answer:
16n¹⁰
![Page 137: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/137.jpg)
ZERO AND NEGATIVE EXPONENTSANYTHING TO THE ZERO POWER IS 1.
271
313
91
313
31
313
13
33
93
273
33
22
11
0
1
2
3
22222
222
41
21
)2(1)2(
2122
xxxx
xxx
813131
311
311
31 4
4
4
4
4
![Page 138: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/138.jpg)
DIVISION PROPERTIES QUOTIENT OF POWERS
This property is used when dividing two or more exponential expressions with the same base.
))()(())()()()((
3
5
xxxxxxxx
xx
2
1))(( xxx
7434
34
3
4
3 11111
xxxx
xxx
xx
![Page 139: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/139.jpg)
DIVISION PROPERTIESPOWER OF A QUOTIENT
12
8
43
424
3
2
)()(
yx
yx
yx
Hard Example
3
43
2
32
yxxy
343
32
)3()2(
yxxy
1293
633
32
yxyx
69
123
278
yxyx
69
123
278
yxyx
6
6
278
xy
![Page 140: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/140.jpg)
ZERO, NEGATIVE, AND DIVISION PROPERTIES
Zero power 1)( 0 x
Negative Exponents
aa
aa
xx
andx
x
1
1
Quotient of powers
bab
a
xxx
Power of a quotient
a
aa
yx
yx
![Page 141: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/141.jpg)
Problems
Are you ready?3, 2, 1…lets go!
![Page 142: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/142.jpg)
Simplify. Your answer should contain only positive exponents.
3r³2r
![Page 143: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/143.jpg)
Answer:
3r²2
![Page 144: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/144.jpg)
Simplify. Your answer should contain only positive exponents.
3xy 5x²( )
2
![Page 145: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/145.jpg)
Answer:
9y²25x²
![Page 146: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/146.jpg)
Simplify. Your answer should contain only positive exponents.
18x⁸y⁸ 10x³
![Page 147: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/147.jpg)
Answer:
9x⁵y⁸5
![Page 148: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/148.jpg)
Simplify:
(x⁴y¯²)(x¯¹y⁵)
![Page 149: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/149.jpg)
Answer:
x³y³
![Page 150: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/150.jpg)
Simplify the following algebraic expression using the distributive property:
8x (6x + 6)∙
![Page 151: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/151.jpg)
Answer:
48x² + 48x
![Page 152: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/152.jpg)
Simplify the following algebraic expression using the distributive property:
7n(6n + 3)
![Page 153: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/153.jpg)
Answer:
42n² + 21n
![Page 154: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/154.jpg)
Simplify the following algebraic expression using the distributive property:
2(9x – 2y)
![Page 155: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/155.jpg)
Answer:
18x – 4y
![Page 156: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/156.jpg)
Simplify the following algebraic expression using the distributive property:
1 + 7(1 – 3b)
![Page 157: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/157.jpg)
Answer:
8 - 21b
![Page 158: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/158.jpg)
Simplify the following algebraic expression using the distributive property:
-2 - 7(-1 – 3b)
![Page 159: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/159.jpg)
Answer:
5 + 21b
![Page 160: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/160.jpg)
Simplify the following algebraic expression using the distributive property:
3n(n² - 6n + 5)
![Page 161: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/161.jpg)
Answer:
3n³ - 18n² + 15n
![Page 162: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/162.jpg)
Simplify the following algebraic expression using the distributive property:
2k³(2k² + 5k - 4)
![Page 163: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/163.jpg)
Answer:
4k⁵ +10k⁴ - 8k³
![Page 164: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/164.jpg)
Simplify the following algebraic expression using the distributive property:
9(x² + xy – 8y²)
![Page 165: Algebraic Expressions 2x + 3y - 7](https://reader034.vdocuments.mx/reader034/viewer/2022052206/5a4d1ad37f8b9ab0599721df/html5/thumbnails/165.jpg)
Answer:
9x² + 9xy – 72y²
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Simplify the following algebraic expression using the distributive property:
9v²(u² + uv - 5v²)
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Answer:
9v²u² +9v³u – 45v⁴
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Simplify the following algebraic expression using the distributive property:
3x(5x+2) - 14(2x²-x+1)
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Answer:
-13x² + 20x - 14
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Simplify completely:
4x²y2x
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Answer:
2xy
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Simplify completely:
y¯¹ y¯²
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Answer:
y
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Simplify completely:
16x⁴y¯¹4x²y¯²
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Answer:
4x²y
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Simplify completely:
36x³y⁶z¹²4x¯¹y³z¹⁰
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Answer:
9x⁴y³z²
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Simplify completely:
21x³y⁷z¹⁴ 30x³z¯⁵18x⁴y⁶ y¹²z¯⁶·
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Answer:
35x²z¹⁵y¹¹