Unit 1 Relationships Between Quantities and Expressions Week 1 Lesson 4 - Multiplying Polynomial Expressions.

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Presentation transcript:

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 situation B.Explain what each term means C.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 expressions equal?

Multiply with Algebra Tiles

Multiply with Algebra Tiles 2x(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(4x 2 + 3x – 5) B.8x 2 + 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 1.2x – 12x 2 – 7 + ½ 2.(2n 3 + 5t) + (9n 3 – 7t + 4) 3.(5x 2 + 3) – (5 – 12x 2 ) 4.4(x 2 + 2x – 8) 5.(2x + 3)(-x + 4)