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**Two Similar Approaches Basic Distributive Property**

Name: Date: Period: Topic: Multiplying Polynomials Essential Questions: How can you use the distributive property to solve for multiplying polynomials? Two Similar Approaches Basic Distributive Property FOIL

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**Home-Learning Review:**

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**1st method: Basic Distributive Property**

Example #1: 2x (5x + 8) Using the distributive property, multiply 2x(5x + 8) = 10x2 + 16x Example #2: -2x2 (3x2 – 7x + 10) = -6x4 + 14x3 – 20x2

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**Can you make a connection from a previous lesson?**

What do you remember about multiplying monomials? What do you do with the coefficients? What about the exponents?

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**Pair-Practice: 1) r (5r + r2) 2) 5y (-2y2 – 7y)**

3) -cd2 (3d + 2c2d – 4c)

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**Simplifying 4(3d2 + 5d) – d(d2 -7d + 12)**

y(y- 12) + y(y + 2) + 25 = 2y (y + 5) - 5

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**Pair-Practice: 4) 5n(2n3 + n2 + 8) + n(4 –n)**

5) (4x – 7) = 5(-2x – 9) - 5

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What’s the GCF? 5x3 + 25x2 + 45x

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2nd Method: FOIL The FOIL method is ONLY used when you multiply 2 binomials. It is an acronym and tells you which terms to multiply. 2) Use the FOIL method to multiply the following binomials: (y + 3)(y + 7).

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2nd Method: FOIL (y + 3)(y + 7). F tells you to multiply the FIRST terms of each binomial. y2

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**(y + 3)(y + 7). O tells you to multiply the OUTER terms of each binomial.**

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**(y + 3)(y + 7). I tells you to multiply the INNER terms of each binomial.**

y2 + 7y + 3y

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**(y + 3)(y + 7). L tells you to multiply the LAST terms of each binomial.**

y2 + 7y + 3y + 21 Combine like terms. y2 + 10y + 21

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**Remember, FOIL reminds you to multiply the:**

First terms Outer terms Inner terms Last terms

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Pair-Practice: 6) (7x – 4)(5x – 1) 7) (11a – 6b)(2a + 3b)

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**What does this mean? How do I solve this type of Binomial?**

Squaring a binomial What does this mean? How do I solve this type of Binomial? (x + 5)2

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Pair-Practice: 8) (x – 3)2

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**Challenge: (6x2 – 2) (3x2 + 2x + 4) (3x2 + 2x + 4) 6x2 – 2**

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(3x2 – 4x + 4) (2x2 + 5x + 6) 3x2 (2x2 + 5x + 6) – 4x (2x2 + 5x + 6) + 4 (2x2 + 5x + 6)

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**Pair-Practice: 9) (8x2 – 4) (2x2 + 2x + 6)**

10) (7x2 – 3x + 5) (x2 + 3x + 2)

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Important: By learning to use the distributive property, you will be able to multiply any type of polynomials. We need to remember to distribute each term in the first set of parentheses through the second set of parentheses.

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**Time to work…independently.**

– x3 (9x4 – 2x3 + 7) (x+5)(x-7) (2x+4)(2x-3) (2x – 7)(3x2+x – 5) (x – 4)2

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Additional Practice: Page 482 – 483 (1, 13, 14, 30) Page 489 – 490 (1, 3, 19, 38) Page 495 – 496 (2, 3, 16, 30, 49)

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**HLA#2: Multiplying Polynomials**

Page 483 (33) Page 489 – 491 (2, 18, 51) Page 496 – 497 (42, 59)

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5.4 Multiplying Polynomials

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