Basic Mathematics for College Students

We can use the distributive property to find the opposite of a sum. For example,

to find , we interpret the symbol as a factor of , and proceed as follows:

Replace the symbol with.

Distribute the multiplication by.

In general, we have the following property.

The Opposite of a Sum

The opposite of a sum is the sum of the opposites.

For any numbers and ,

(ab)a(b)

a b

x 10

 1 (x)( 1 )(10)  1

(x10) 1 (x10)   1



(x10)   1

652 Chapter 8 An Introduction to Algebra

b.This expression contains three factors.

Multiply 2 and 8 to get 16.

Distribute the multiplication by 16.

c.

0.9a1.2b2.1 Do each multiplication.

0.3(3a 4 b7)0.3(3a)(0.3)(4b)(0.3)(7)

 16 a 48 b

16(a 3 b)

 

2(a 3 b) 8  2  8 (a 3 b)

Use the commutative property of

multiplication to reorder the factors.

0

2

.3

 7

2.1

0

1

.3

 4

1.2

0.3

 3

0.9

EXAMPLE (^5) Simplify:
StrategyWe will multiply each term within the parentheses by.
WHYThe outside the parentheses represents a factor of that is to be
distributed.
Solution
Distribute the multiplication by.
Do the multiplications. Try to go
directly to this step.
 9 s 3
 1 ( 9 s)( 1 )(3)  1
Replace the symbol in front
( 9 s3) 1 ( 9 s3) of the parentheses with 1.

  1

 1

( 9 s3)

Identify like terms.

Before we can discuss methods for simplifying algebraic expressions involving

addition and subtraction, we need to introduce some new vocabulary.

Like Terms

Like termsare terms containing exactly the same variables raised to exactly

the same powers. Any constant terms in an expression are considered to be

like terms. Terms that are not like terms are called unlike terms.

3

Self Check 5

Simplify:

Now TryProblem 59

( 5 x18)