Since subtraction is the same as adding the opposite, the distributive property also
holds for subtraction.
a(bc)abac
650 Chapter 8 An Introduction to Algebra
Self Check 2
Multiply:
a.
b.
c.
Now TryProblems 35, 37, and 39
24 a
y
6
3
8
b
80(8x3)
7(m2)
EXAMPLE 2
Multiply: a. b. c.
StrategyIn each case, we will distribute the multiplication by the factor outside
the parentheses over each term withinthe parentheses.
WHYIn each case, we cannot simplify the expression within the parentheses. To
multiply, we must use the distributive property.
Solution
a.We read as “eight times the quantityof plus nine.” The word
quantityalerts us to the grouping symbols in the expression.
Distribute the multiplication by 8.
Do the multiplications. Try to go directly to this step.
b. Distribute the multiplication by 12.
Do the multiplications.
c. Distribute the multiplication by 6.
2 x 27
Factor 6 as 23 and then remove
the common factors 3 and 2.
2 3
1
x
3
1
2
1
3 9
2
1
6 a
x
3
9
2
b 6
x
3
6
9
2
Write the result in simpler form. Recall that
48 t (^12) adding 12 is the same as subtracting 12.
48 t(12)
12 (4t1) 12 (4t)( 12 )(1)
8 m 72
8 (m9) 8 m 8 9
8(m9) m
6 a
x
3
9
2
8(m9) 12(4t1) b
12
4
48
EXAMPLE 3
Multiply: a. b. c.
StrategyIn each case, we will distribute the multiplication by the factor outside
the parentheses over each term withinthe parentheses.
WHYIn each case, we cannot simplify the expression within the parentheses. To
multiply, we must use the distributive property.
Solution
a. Distribute the multiplication by 3.
Do the multiplications. Try to go directly to this step.
Caution! A common mistake is to forget to distribute the multiplication over
each of the terms within the parentheses.
3(3b4) 9 b 4
9 b 12
3 (3b4) 3 (3b) 3 (4)
3(3b4) 6( 3 y8) 1(t9)
Self Check 3
Multiply:
a.
b.
c.
Now TryProblems 43, 47, and 49
1(c22)
9(y4)
5(2x1)