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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)
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