Page 586 - Basic College Mathematics with Early Integers

S E C T I O N 8.1 I VARIABLE EXPRESSIONS 563

Examples Multiply. PRACTICE 11–12
Multiply.
11. 513y2 = 15 32y Apply the associative property of multiplication.
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11. 7(8a)
= 15y Multiply.
12. -519x2
12. -214x2 = 1-2 42x Apply the associative property of multiplication.
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=-8x Multiply.
Work Practice 11–12
We can use the distributive property to combine like terms, which we have
done, and also to multiply expressions such as 213 + x2. By the distributive prop-
erty, we have that

2(3+x)=2 3+2 x Apply the distributive property.
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= 6 + 2x Multiply.
Example 13 Use the distributive property to multiply: 61x + 42 PRACTICE 13
Use the distributive property to
Solution: By the distributive property, multiply: 71y + 22

6(x+4)=6 x+6 4 Apply the distributive property.
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= 6x + 24 Multiply.
Work Practice 13

Concept Check What’s wrong with the following?
81a - b2 = 8a - b

Example 14 Multiply: -315a + 22 PRACTICE 14
Multiply: 417a - 52
Solution: By the distributive property,

–3(5a+2)=–3(5a)+(–3)(2) Apply the distributive property.
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= 1-3 52a + 1-62 Apply the associative property.Also, write 1-32122 as -6.
=-15a - 6 Multiply.

Work Practice 14
PRACTICE 15
Objective Simplifying Expressions
Simplify: 512y - 32 - 8
Next, we will simplify expressions containing parentheses by first using the distribu-
tive property to multiply and then combining any like terms.
Example 15 Simplify: 213 + 7x2 - 15 2 is not distrib-
uted to the -15 since it is not
Solution: First we use the distributive property to remove parentheses. within the parentheses.

2(3+7x)-15=2(3)+2(7x)-15 Apply the distributive property. Answers
= 6 + 14x - 15 Multiply. 11. 56a 12. -45x 13. 7y + 14
14. 28a - 20 15. 10y - 23
= 14x + 1-92 or 14x - 9 Combine like terms.
Concept Check Answer
Work Practice 15 did not distribute the 8