Distributive PropertyDistributive PropertyMultiply across ParenthesesMultiply across Parentheses

3(x + 4) = 3(x) + 3(4)3(x + 4) = 3(x) + 3(4) 3x + 123x + 12

Think of it as looking to Think of it as looking to DISTRIBUTE something something

Remember This???

Remember This???

Evaluate Evaluate A.A. 3(x + 7)3(x + 7)

B.B. a(a + b)a(a + b)

C.C. 10(x + 2y - z)10(x + 2y - z)

A). 3(x) + 3(7) A). 3(x) + 3(7)

3x + 21 3x + 21

B). a(a) + a(b) B). a(a) + a(b)

a² + aba² + ab

C). 10(x) + 10(2y) - 10(z)C). 10(x) + 10(2y) - 10(z)

10x + 20y - 10z10x + 20y - 10z

ObjectiveObjective

SWBAT multiply polynomialsSWBAT multiply polynomials

Section 9.2 “Multiply Polynomials” Section 9.2 “Multiply Polynomials” When multiplying polynomials use the When multiplying polynomials use the distributive property. Distribute and multiply distributive property. Distribute and multiply each term of the polynomials. Then simplify. each term of the polynomials. Then simplify.

2x2x³³(x(x³ + 3x² - 2x + 5)³ + 3x² - 2x + 5)

62x 56x 44x 310x3456 10462 xxxx

3c3c³³(8c(8c³ - c² - 3c + 5)³ - c² - 3c + 5)624c 53c 49c 315c

3456 159324 cccc

Try It Out…Try It Out…

““Multiply Using FOIL” Multiply Using FOIL” When multiplying a binomial and another When multiplying a binomial and another polynomial use the method. polynomial use the method. FOIL

FirstFirst OuterOuter InnerInner LastLast

(x – 4)(x – 4)(3x + 2(3x + 2))

23x x2 x12 8

8103 2 xx

““Multiply Using FOIL”Multiply Using FOIL”

combine like terms

(3a + 4)(3a + 4)(a – 2(a – 2))

23a a6 a4 8

823 2 aa

““Multiply Using FOIL”Multiply Using FOIL”

combine like terms

(4x – 5)(4x – 5)(2x(2x² + 5x – 1)² + 5x – 1)

38x 220x x4210x

529108 23 xxx

x25 5 combine like terms

The Product of a Binomial and Trinomial…The Product of a Binomial and Trinomial…

(b – 2)(b – 2)(b(b² - b + 1)² - b + 1)

3b 2b b22b

233 23 bbb

Try It Out…Try It Out…

b2 2combine like terms

Simplifying Polynomials in Simplifying Polynomials in GeometryGeometry

What is the area of the blue region?What is the area of the blue region?

3x – 2

2x + 144

1010

FOIL

(3x – 2)(2x + 1)

6x² – x – 2

4 x 10 = 40

6x² – x – 2 – 40 = 6x² – x – 42

HomeworkHomework

Text p. 565, #4-48 multiples of 4, & #50Text p. 565, #4-48 multiples of 4, & #50