lesson 9 multiply polynomials.notebook...lesson 9 multiply polynomials.notebook let's review...
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![Page 1: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/1.jpg)
Lesson 9 Multiply Polynomials.notebook
Let's Review
Adding and Subtracting Polynomials.Combining Like Terms
2x + 3x = (2 + 3)x = 5x
3x2 + 2x2 = (3 + 2)x 2 = x 2
Remember that Combining Like Terms is an application of the Distributive Property.
2x2 2 + 4x x2 x + 5
(4x2 3x + 2 ) + (3x2 + x 4)
This means addition, NOT multiplication!
x2 + 3x + 5
4x2 - 3x + 2 - 3x2 + x - 4x2 - 2x - 2
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Lesson 9 Multiply Polynomials.notebook
)( 3x2 - 2x + 4 + )( -2x2 + 6x + 5
1) Distinguish the like terms
)( + 4 + )(
2) Group the like terms
3x2 -2x2 - 2x
+ 6x
+ 5
3x2 -2x2 - 2x
+ 6x
+ 4 + 5
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Lesson 9 Multiply Polynomials.notebook
)( + 4 + )(
3) Combine the like terms
3x2 -2x2 - 2x
+ 6x
+ 5
3x2 -2x2 - 2x
+ 6x
+ 4 + 5
x2 + 4x 9 +
How can we model this subtraction?(2x2 + 4x – 5) – (x2 + 2x – 3)
Hint: Remember that when you subtract, you are actually adding the opposite!
(2x2 + 4x - 5) + (-x2 - 2x + 3)
x2 + 2x - 2
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Lesson 9 Multiply Polynomials.notebook
(n 12) (n2 + n + 9)
n - 12 - n2 - n - 9-n2 - 21
Distribute the negative, then combine like terms.
(n 3) 2(n2 4n + 5)
Now lets complicate it a little.
n - 3 - 2n2 + 8n - 10 -2n2 + 9n - 13
![Page 5: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/5.jpg)
Lesson 9 Multiply Polynomials.notebook
4(n 3) 2(n2 4n + 5) + 8
Now lets complicate it a little more.
4n - 12 - 2n2 + 8n - 10 + 8 -2n2 + 12n - 14
Multiplying a Monomial by a Polynomial (with more than one term)
2x(x2 + 3x - 6)
Use the Distributive Property.
2x3 + 6x2 - 12x
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Lesson 9 Multiply Polynomials.notebook
Multiplying a Binomial by a BinomialUse the Distributive Property.
(2x - 5)(3x + 8)
(f + 2)2
2x(3x + 8) - 5(3x + 8)6x2 + 16x - 15x - 406x2 + x - 40
(f + 2)(f + 2)f(f + 2) + 2(f + 2)f2 + 2f + 2f + 4f2 + 4f + 4
(m2 - 4)(m3 + 2m2 - 7m + 3)
What's the difference??
(m2 - 4) + (m3 + 2m2 - 7m + 3)Addition
Multiplication
![Page 7: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/7.jpg)
Lesson 9 Multiply Polynomials.notebook
n[(n + 2)(n 2) 4]
Find the degree.
5m2n3
3x3y + xy 4
![Page 8: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/8.jpg)
Lesson 9 Multiply Polynomials.notebook
Use Eraser to check the answers
Do Now
Problem Set
![Page 9: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/9.jpg)
Lesson 9 Multiply Polynomials.notebook
![Page 10: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/10.jpg)
Lesson 9 Multiply Polynomials.notebook
Use Eraser to check the answers
Lesson 9Generating PolynomialsMultiply Polynomials
Student Outcomes § Students understand that the product of two polynomials produces another polynomial; students multiply polynomials.
![Page 11: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/11.jpg)
Lesson 9 Multiply Polynomials.notebookClasswork Exercise 1 (15 minutes)
Answer
Answer
What do you notice about the terms along the diagonals in the rectangles you drew?
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Lesson 9 Multiply Polynomials.notebook
Answer
What do you notice about the terms along the diagonals in the rectangles you drew?
Answer
What do you notice about the terms along the diagonals in the rectangles you drew?
![Page 13: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/13.jpg)
Lesson 9 Multiply Polynomials.notebook
Encourage students to recognize that in parts b and c the terms along the diagonals were all like terms, however, in part d one of the factors has no xterm. Allow students to develop a strategy for dealing with this, concluding with the suggestion of inserting the term +0x, for a model that looks like the following:
Students may naturally ask about the division of polynomials. This topic will be covered in Grade 11, Module 1. The extension challenge at the end of the lesson, however, could be of interest to students inquiring about this.
Could we have found this product without the aid of a geometric model? What would that look like?
Use the Distributive Property and collect like terms.
Also remind students that variables are placeholders for numbers. If x = 5 then the right side is= 270 and the 5 1 of "that quantity" or 5 of that quantity minus 1 of that quantitty
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Lesson 9 Multiply Polynomials.notebook
Exercise 2 (5 minutes)Students work independently then compare answers with a neighbor. Discuss and justify answers.
Exercise 3 (10 minutes) Give students 10 minutes to complete Exercise 3 and compare their answers with a neighbor.
Answer
![Page 15: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/15.jpg)
Lesson 9 Multiply Polynomials.notebook
Answer
Answer
![Page 16: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/16.jpg)
Lesson 9 Multiply Polynomials.notebook
Answer
Answer
![Page 17: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/17.jpg)
Lesson 9 Multiply Polynomials.notebook
Exercise 4 (5 minutes)
Answer
![Page 18: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/18.jpg)
Lesson 9 Multiply Polynomials.notebook
Answer
Answer
Problem SetUse eraser to check answers
![Page 19: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/19.jpg)
Lesson 9 Multiply Polynomials.notebookUse eraser to check answers
Use eraser to check answers
![Page 20: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/20.jpg)
Lesson 9 Multiply Polynomials.notebookUse eraser to check answers
Use eraser to check answers
![Page 21: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/21.jpg)
Lesson 9 Multiply Polynomials.notebook
Use eraser to check answers
(a + b)(a + b) (a + 1)(a + 1) (3 + b)(3 + b)
Use eraser to check answers
![Page 22: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/22.jpg)
Lesson 9 Multiply Polynomials.notebook
Use eraser to check answers
Use eraser to check answers
![Page 23: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/23.jpg)
Lesson 9 Multiply Polynomials.notebook
Use eraser to check answers
Use eraser to check answers
![Page 24: Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding and Subtracting Polynomials. Combining Like Terms 2x + 3x = (2 + 3)x = 5x 3x2 +](https://reader036.vdocuments.mx/reader036/viewer/2022070901/5f4e5cb3be35eb2033465abe/html5/thumbnails/24.jpg)
Lesson 9 Multiply Polynomials.notebook
Use eraser to check answers
Use eraser to check answers