2.7 Using the Distributive Property

• Goal:

1.)To multiply using the distributive property of multiplication over subtraction

2.)To factor

Distributive PropertyDistributive Property

SUBTRACTIONSUBTRACTION

a(b - c) = ab - aca(b - c) = ab - ac

a(b - c) a(b - c) and ab - ac ab - ac are equivalent expressions

Distributive PropertyDistributive Property

SUBTRACTIONSUBTRACTION

3(5 - 2) = 33(5 - 2) = 3••5 5 -- 3 3••22

5 (2x - 3)= - 1510x

-4 (3y - 2)=

+ 8-12y

(3t - 7)6 =

- 4218t

-7(5y - 4) =

+28

-35y

3.1 (2.5 x – 3 + 4.5y)

Answer: 7.75 x + (-9.3) + 13.95 y

-7/8 (2/3x – 1/2y -8)

Answer: -7/12x + 7/16y +7

FactoringFactoring

aab - b - aacc = = aa(b - c) (b - c)

Distributive PropertyDistributive Property

a(b - c) = ab - aca(b - c) = ab - ac

Factoring

• The word factor means to divide

• You are looking to find a # that is divisible by the all of the numbers

• Set up this form:

____ ( ____ + ____) or ____ (____ + ___ +___)

Tricks to Factoring

• Pick the smallest number you and try to divide it by the rest of the numbers

• If that does not work divide the smallest number by 2 or 3 or 5 then see if that number is divisible by the rest

• Make sure you answer is completely factored

Factor: 10x - 15y

5(2x - 3y)

Factor: 12x - 8

4(3x - 2)

Factor: 9x + 27y - 18

9(x + 3y - 2)

Factor: 12 - 3x

3(4 - x)

Factor:

ua – ub – uc

ua + - ub + - uc

u (a+-b +-c)

Factor:

2p – 1q- 5r

3 3 3

When you are asked to factor fractions you are going to factor out 1 over the cd and write the numerators in the ( )

1/3 (2p +- 1q + - 5r)

Assignment:

Page 911-26 Show all work!!