Page 584 - Basic College Mathematics with Early Integers

S E C T I O N 8.1 I VARIABLE EXPRESSIONS 561

Concept Check True or false? The terms -7xy and -7yx are like terms.
Explain.
A sum or difference of like terms can be simplified using the distributive prop-
erty. Recall from Section 1.6 that the distributive property says that multiplication
distributes over addition (and subtraction). Using variables, we can write the
distributive property as follows:

(a+b)c=ac+bc.

If we write the right side of the equation first, then the left side, we have the following:

Distributive Property
If a, b, and c are numbers, then
ac + bc = 1a + b2c

Also,
ac - bc = 1a - b2c

The distributive property guarantees that, no matter what number x is, 7x + 5x
(for example) has the same value as 17 + 52x, or 12x. We then have that

7x + 5x = 17 + 52x = 12x

This is an example of combining like terms. An algebraic expression is
simplified when all like terms have been combined.

Example 5 Simplify each expression by combining like terms. PRACTICE 5
Simplify each expression by
a. 3x + 2x b. y - 7y
combining like terms.
Solution: We add or subtract like terms. a. 8m - 11m
a. 3x + 2x = 13 + 22x b. 5a + a
= 5x

Understood 1
b. y-7y=1y-7y
= 11 - 72y
=-6y

Work Practice 5

The commutative and associative properties of addition and multiplication can
also help us simplify expressions. We presented these properties in Sections 1.3 and
1.6 and state them again using variables. Answers
5. a. -3m b. 6a

Concept Check Answer
true; the order of the variable factors
does not make a difference