Unit 1 Relationships Between Quantities and Expressions

Week 1

Lesson 4 - Multiplying Polynomial Expressions

Today’s Objective• A.SSE.1 – Interpret parts of an expression• A.APR.1 – Add, subtract, and multiply

polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.

• Students will Multiply polynomial expressions

Essential Questions

• What is the distributive property?• What does it mean to distribute something?• How do you apply the distributive property?• Will the product of 2 polynomials produce

another polynomial?

Vocabulary

• Simplify• Like Terms• Polynomial• Polynomial Expression• Distributive Property

Read, Draw, Write, Solve

Hunter loves to do math problems and is getting more efficient in his work. He wants to work on his math after school each day for 30 minutes.

A. Write an expression that can model this situationB. Explain what each term meansC. How many minutes will Hunter spend working on

math after 6 days?D. How many total hours will it be?

“Polynomials are closed under addition, subtraction and

multiplication”

If you multiply polynomials with polynomials you will get more

polynomials!

Distributive Property

• Discuss at your table what you think the steps would be to simplify expression A, B and C and simplify each one.

A. 2 + (x + 3)B. 2 - (x + 3)C. 2(x + 3)

Let’s see how we can use our algebra tiles to apply the distributive property.

2x(x + 3) = ?

Are the two expressionsequal?

Multiply with Algebra Tiles

Multiply with Algebra Tiles2x(x – 2)

Multiply with Algebra Tiles(2x – 1)(x + 3)

Multiply with Algebra Tiles(2x + 1)2

Remember how to multiply using an area model?

23 x 3

Remember how to multiply using an area model?

21 x 35

Remember how to multiply using an area model?

2x(x – 2)

Remember how to multiply using an area model?

(2x + 1)(x + 3)

Remember how to multiply using an area model?

(x - 1)(x – 4)

Remember how to multiply using an area model?

(2x - 1)(x + 3)

Practice

• Let’s try some more examples and you choose the method that works best for you.

• Traditional Distributive Property• Algebra Tiles• Area Model

What is the perimeter of the rectangle?

What is the area of the rectangle?

What is the area of the rectangle?

What is the perimeter of the rectangle?

Are the two Polynomial Expressions below equivalent? Explain why or why not.

A. 2(4x2 + 3x – 5)B. 8x2 + 6x – 10

Are the two Polynomial Expressions below equivalent? Explain why or why not.

A. -2(3x – 3) B. -6x – 18

Exit Ticket – Lesson 4

• Simplify the Polynomial Expressions

1. 2x2 + 4 – 12x2 – 7 + ½ 2. (2n3 + 5t) + (9n3 – 7t + 4)3. (5x2 + 3) – (5 – 12x2)4. 4(x2 + 2x – 8)5. (2x + 3)(-x + 4)