SECTION 1.7 Properties of Real Numbers^65
(f )
Distributive property in reverse
Add.
Multiply.(g)
Distributive property in reverse(h)
= 61 x- 22 Distributive property in reverse NOW TRY
= 6 #x- 6 # 2
6 x- 12
= 41 x- m 2
4 x- 4 m
= 60
= 61102
= 618 + 22
6 # 8 + 6 # 2
Using the Distributive PropertyUse the distributive property to rewrite each expression.
(a)
Distributive property
Multiply.= 75 Add.
= 45 + 30
= 5 # 9 + 5 # 6
519 + 62
EXAMPLE 9
Multiply first.(b)
Distributive property
Multiply.(c)
Distributive property=- 2 x- Multiply.
3
2
=-
1
2
14 x 2 + a-
1
2
b1 32
-
1
2
14 x+ 32
= 4 x+ 20 + 4 y
= 4 x+ 4 # 5 + 4 y
41 x+ 5 + y 2
Think: -^12 (4x)=A-^12 # 4 B x=A-^12 #^41 B x
(d)
Definition of subtraction
Distributive property
Multiply.(e)
Distributive property
Associative property= 24 r+ 88 t+ 40 z Multiply.
= 18 # 32 r + 18 # 112 t+ 18 # 52 z
= 813 r 2 + 8111 t 2 + 815 z 2
813 r+ 11 t+ 5 z 2
= 3 k- 27
= 3 k+ 31 - 92
= 33 k+ 1 - 924
31 k- 92
NOW TRY
EXERCISE 9
Use the distributive property
to rewrite each expression.
(a)
(b)
(c) 5 x- 5 y
612 r+t- 5 z 2- 514 x+ 12
NOW TRY ANSWERS
- (a)
(b)
(c) 51 x-y 2
12 r+ 6 t- 30 z- 20 x- 5
CAUTION In practice, we often omit the first step in Example 9(d),where we
rewrote the subtraction as addition of the additive inverse.
Be careful not to make a sign error.