Basic Mathematics for College Students

Here are several examples.

Like terms Unlike terms

and and The variables are not the same.

and and Same variable, but different powers.

and and The variables are not the same.

Success Tip When looking for like terms, don’t look at the coefficients of the

terms. Consider only the variable factors of each term. If two terms are like

terms, only their coefficients may differ.

c^3

1

3

c^3 d c^3 d

1

3

c^3 d

 10 p^225 p^2  10 p 25 p^2

4 x 7 x 4 x 7 y

8.2 Simplifying Algebraic Expressions 653

Self Check 6

Identify the like terms:

a.

b.

Now TryProblem 63

5 p^2  12  17 p^2  2

2 x 2 y 7 y

EXAMPLE (^6) Identify the like terms in each expression:
a. b. c.
StrategyFirst, we will identify the terms of the expression. Then we will look for
terms that contain the same variables raised to exactly the same powers.
WHYIf two terms contain the same variables raised to the same powers, they are
like terms.
Solution
a. contains the like terms and.
b.Since the exponents on are different, contains no like terms.
c. contains two pairs of like terms: and are like
terms, and the constant terms, 3 and  2 , are like terms.
 17 m^3  3  2 m^3  17 m^3 m^3
x 6 x^4  6 x^2  6 x
7 r 5  3 r 7 r 3 r
7 r 5  3 r 6 x^4  6 x^2  6 x  17 m^3  3  2 m^3
Combine like terms.
To add or subtract objects, they must be similar. For example, fractions that are to be
added must have a common denominator. When adding decimals, we align columns to
be sure to add tenths to tenths, hundredths to hundredths, and so on. The same is true
when working with terms of an algebraic expression. They can be added or subtracted
only if they are like terms.
This expression can be simplified This expression cannotbe simplified
because it contains like terms. because its terms are not like terms.
Recall that the distributive property can be written in the following forms:
We can use these forms of the distributive property in reverse to simplify a sum or
difference of like terms. For example, we can simplify as follows:
Use the form:.
Success Tip Just as 3 apples plus 4 apples is 7 apples,
3 x 4 x 7 x
 7 x
3 x 4 x( 3  4 )x baca(bc)a
3 x 4 x
(bc)abaca (bc)abaca
3 x 4 x 3 x 4 y
4