Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding...

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


)( 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


)( + 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


(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


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


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


n[(n + 2)(n 2) 4]

Find the degree.

5m2n3

3x3y + xy 4


Use Eraser to check the answers

Do Now

Problem Set


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.

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?


Answer


Answer



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


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


Answer

Answer


Exercise 4 (5 minutes)

Answer


Answer

Answer

Problem SetUse eraser to check answers

Lesson 9 Multiply Polynomials.notebookUse eraser to check answers

Use eraser to check answers



(a + b)(a + b) (a + 1)(a + 1) (3 + b)(3 + b)


Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding...

Documents

Transcript of Lesson 9 Multiply Polynomials.notebook...Lesson 9 Multiply Polynomials.notebook Let's Review Adding...