2 7 The Distributive Property Simplify by using

2. 7 The Distributive Property

Simplify by using the Distributive Property 6 ( 3 x + 5 ) = 6 ● 3 x + 6 ● 5 = 18 x + 30

Simplify by using the Distributive Property 5 ( 2 + 7 y ) = 5 ● 2 + 5 ● 7 y = 10 + 35 y = 35 y + 10

Simplify by using the Distributive Property -4 ( 8 a - 9 )

Simplify by using the Distributive Property -5(x – 3 y +8 z)

Simplify by using the Distributive Property 4( s – t + w ) 3

Simplify by using the Distributive Property 5( x – 3 y + 8 z) 6

Factoring l The reverse of multiplying l Factor out the greatest common factor (GCF) of all terms

Factor 5 x + 5 y = 5(x + y)

Factor 9 x + 27 y = 9 x + 9 (3 y) = 9 (x + 3 y)

Factor 18 a + 21 b = 3(6 a) + 3(7 b) = 3 (6 a + 7 b)

Factor 5 x – 35 y – 10

Try on your own… Factor - 25 y + 15 w + 5

What is a term? l Terms are separated by addition or subtraction What are these terms called? x - 15 + 8 y coefficient Variable term Constant. Variable Term

What are “like terms”? same VARIABLE and same EXPONENT 2 x + 5 x LIKE TERMS 27 - 6 z NOT LIKE TERMS

What are “like terms”? same VARIABLE and same EXPONENT w² + w NOT LIKE TERMS 3 m + m 20 m LIKE TERMS

Combine like terms 5 x + 4 x + 2 x add coefficients = 11 x

Combining Like Terms 1. Change all subtraction to adding the opposite. 2. Combine like terms. 5 x - (-9) + 2 x + 7 = 5 x + 9 + 2 x + 7 = 7 x + 16