Basic Mathematics for College Students

We can simplify in a similar way:

Use the form:.

The Language of Algebra Simplifying a sum or difference of like terms is

called combining like terms.

These examples suggest the following general rule.

Combining Like Terms

Like terms can be combined by adding or subtracting the coefficients of the

terms and keeping the same variables with the same exponents.

 6 m^2

15 m^2  9 m^2 ( 15  9 )m^2 baca(bc)a

15 m^2  9 m^2

654 Chapter 8 An Introduction to Algebra

EXAMPLE (^7) Simplify by combining like terms, if possible:
a. b. c. d. e.
StrategyWe will use the distributive property in reverse to add (or subtract) the
coefficients of the like terms. We will keep the same variables raised to the same
powers.
WHYTo combine like terms means to add or subtract the like terms in an
expression.
Solution
a.Since and are like terms with the common variable , we can combine
them.
Think:.
b. Think:.
c. Think:.
d.Since and 6 are not like terms, they cannot be combined. The expression
doesn’t simplify.
e. Think:. 149 ^792 b^119 b

4

9

b

7

9

b

11

9

b

4 w 6

4 w

0.5s^3 0.3s^3 0.2s^3 (0.50.3)s^3 0.2s^3

 8 p( 2 p) 4 p 6 p [ 8 (2)4]p 6 p

2 x 9 x 11 x (29)x 11 x

2 x 9 x x

4

9

b

7

9

2 x 9 x  8 p( 2 p) 4 p 0.5s^3 0.3s^34 w 6 b

Self Check 7

Simplify, if possible:

a.

b.

c.

d.

e.

Now TryProblems 67, 71, 79, and 83

10

7

c

4

7

c

4 a 2

4.4s^4 3.9s^4

 6 y( 6 y) 9 y

3 x 5 x

Self Check 8

Simplify:

a. b.

c. d.

Now TryProblems 73 and 77

9 h 8 h 8 h 9 h

9 hh 9 hh

EXAMPLE (^8) Simplify by combining like terms:
a. b. c. d.
StrategyAs we combine like terms, we must be careful when working with terms
such as and.
WHYCoefficients of 1 and are usually not written.
Solution
a. Think:.
b. Think:.
c. Think:.
d. 16 tt 17 t Think:. 16 t 1 t(161)t 17 t
15 t 16 tt (1516)t 1 tt
16 tt 15 t 16 t 1 t(161)t 15 t
16 t 15 tt (1615)t 1 tt

 1

t t

16 t 15 t 16 tt 15 t 16 t 16 tt