SECTION 1.8 Simplifying Expressions^71
Combining Like TermsCombine like terms in each expression.
(a)
= - 4 m
= 1 - 9 + 52 m
- 9 m+ 5 m
EXAMPLE 2
(b)
Distributive property
Multiply.= 24 k- 12 Combine like terms.
= 9 k- 6 - 6 + 15 k
= 9 k- 6 - 3122 - 31 - 5 k 2
9 k- 6 - 312 - 5 k 2
NOW TRY
EXERCISE 2
Combine like terms in each
expression.
(a) (b)
(c) 4 p^2 - 3 p^2
4 x+ 6 x- 7 x z+z(b)
= 11 r
= 16 + 3 + 22 r
6 r+ 3 r+ 2 r
(c)
= 5 x
= 14 + 12 x
= 4 x+ 1 x x= 1 x
4 x+ x (d)
= 7 y^2
= 116 - 92 y^2
16 y^2 - 9 y^2
(e) 32 y+ 10 y^2 These unlike terms cannot be combined. NOW TRY
CAUTION Remember that only like terms may be combined.
Simplifying Expressions Involving Like TermsSimplify each expression.
(a)
Distributive property
Multiply.= 20 y+ 12 Combine like terms.
= 14 y+ 12 + 6 y
= 14 y+ 2162 + 213 y 2
14 y+ 216 + 3 y 2
EXAMPLE 3
NOW TRY ANSWERS
- (a) 3 x (b) 2 z (c)p^2
(c)
Distributive property
Multiply.=- 2 + 11 r Combine like terms.
=- 2 + 1 r+ 10 r
=- 1122 - 11 - r 2 + 10 r
= - 112 - r 2 + 10 r -a=- 1 #a
- 12 - r 2 + 10 r
(d)
Associative property
Multiply.= 3 x+ 12 Distributive property
= 31 x+ 42
= 3110021 0.03 241 x+ 42
1003 0.03 1 x+ 424
Be careful
with signs.OBJECTIVE 4 Combine like terms.Recall that the distributive property
can be written “in reverse” as
This last form, which may be used to find the sum or difference of like terms, pro-
vides justification for combining like terms.
a 1 b+c 2 =ab+ ac ab+ac =a 1 b+c 2.
Be careful
with signs.