NAME
4-1
DATE
PERIOD
Study Guide and Intervention
The Distributive Property
Numerical Expressions
The expressions 2(1 + 5) and 2 · 1 + 2 · 5 are equivalent
expressions because they have the same value, 12. The Distributive Property combines
addition and multiplication.
Symbols
Model
a(b + c) = ab + ac
a
(b + c)a = ab + ac
b + c
b
c
= a
+ a
Lesson 4-1
The Distributive Property also combines subtraction and multiplication.
Symbols
a(b - c) = ab - ac
(b - c)a = ab - ac
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 1
Use the Distributive Property to write 2(6 + 3) as an equivalent
expression. Then evaluate the expression.
2(6 + 3) = 2 · 6 + 2 · 3
= 12 + 6
Multiply.
= 18
Add.
Example 2
Use the Distributive Property to write 5(9 - 3) as an equivalent
expression. Then evaluate the expression.
5(9 - 3) = 5 · 9 - 5 · 3
= 45 - 15
Multiply.
= 30
Subtract.
Exercises
Use the Distributive Property to write each expression as an equivalent
expression. Then evaluate the expression.
1. 3(8 + 2)
2. 2(9 + 11)
3. 5(19 - 6)
4. -6(3 + 14)
5. (17 - 4)3
6. (5 + 3)7
7. 9(20 + 8)
8. (8 - 3)4
9. 7(40 - 5)
Chapter 4
5
Glencoe Pre-Algebra
NAME
4-1
DATE
Study Guide and Intervention
PERIOD
(continued)
The Distributive Property
Algebraic Expressions The Distributive Property can also be used with algebraic
expressions containing variables.
Example 1
Use the Distributive Property to write 7(m + 5) as an equivalent
algebraic expression.
7(m + 5) = 7m + 7 · 5
= 7m + 35
Simplify.
Example 2
Use the Distributive Property to write 3(n - 8) as an equivalent
algebraic expression.
3(n – 8) = 3[n + (– 8)]
Rewrite n – 8 as n + (–8).
= 3n + 3 · (– 8)
Distributive Property
= 3n + (–24)
Simplify.
= 3n – 24
Definition of subtraction
Exercises
Use the Distributive Property to write each expression as an equivalent
expression.
2. (w - 5)4
3. -2(c + 7)
4. 9(b + 4)
5. ( p - 10)8
6. -11( g - 6)
7. -14( j + 3)
8. (15 - a)20
9. 9(50 + h)
10. 5(12 - c)
11. -12(s - 2)
12. 8(x + 60)
13. ( y - 13)20
14. -15(4 + n)
15. 7(r - 11)
Chapter 4
6
Glencoe Pre-Algebra
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. 3(d + 4)