Distributive Property Multiply across Parentheses 3(x + 4) = 3(x) + 3(4) 3x + 12 3x + 12 Think of it...
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Transcript of Distributive Property Multiply across Parentheses 3(x + 4) = 3(x) + 3(4) 3x + 12 3x + 12 Think of it...
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
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