# 1.7 Distributive Property

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1.7 Distributive Property
AREA
Compare
= length x width
3 x 14
and 3 x (10 + 4)
14 = 10 + 4
10
3
3
3(10 + 4) = 3 x 14 = 42
4
3
3(10 + 4) = 3 x 10 + 3 x 4
= 30 + 12 = 42
Formally, they write this property as "a(b
Examples
+ c) = ab + ac".
a. 2(6 + 3) = 2 · 6 + 2 · 3 =
b. 7(24) = 7(20 + 4)= 140 + 28 = 168
12 + 6 = 18
c. 7(m - 5) = 7m - 35
d. (m + n - 8)3 = 3m + 3n - 24
Use the Distributive Property to write each expression as an equivalent
expression. Then evaluate the expression, if possible.
1. 3(8 + 2)
24 + 6 = 30
2. 2(9 + 11)
18 + 22 = 40
3. (19 – 6)5
95 – 30 = 65
3 _ 8 _ 3 _ 2; 30 2 _ 9 _ 2 _ 11; 40 5 _ 19 _ 5 _ (_6); 65
4. 6(27)
6(20 + 7)= 120 +42=
142
5. 3(38)
3(30 + 8) = 90 + 24=
114
6. (5 + 3)7
7(5) + 7(3) = 35 + 21 = 56
7. 3(d + 4)
8. (w – 5)4
9. 2(c + d + 7)
3d + 12
4w – 20
2c + 2d + 14
Use the Distributive Property to write each expression as an equivalent expression. Then
evaluate the expression.
1. 8(24) = 8(20 + 4)
3. 2(64) = 2( 60 +
2. 19 · 5 = (20 - 1)5
)
4. 7(43) = 7(
+
)
400 _ 32; 432 100 _ 45; 145 120 _ 8; 128 280 _ 14; 266
5. 4(100 – 2)
6. 4(17) =
7. 8(10 + 1)
8. 9 x 24 =
1600 _ 8; 1592 _64 _ 20; _84 _32 _ 8; _40_ 9; _66 294 _ 154; 140 _2000 _ 50; _2050 13,950 _ 558;
13,392
Use the Distributive Property to write each expression as an equivalent algebraic expression.
9. 7( y + 11)
10. 6(t – 1)
11. 8(u – 2)
12. (r + 9)(4)
7y _ 77 _6t _ 6 _8u _ 16 _4r _ 36
13. 1(h + 5)
14. 2( f + g + 3)
15. 4(b – 1)
16. (7 – v)· 1
17. 5(1 – b)
19. 8(q – 5)
20. 4(h – 16)
h _ 5 _2f _ 6 _4b _4 7 _ v
21. 2(d – 5)
22. 2(n + 10 - m)
23. 50(z - 1)
24. 12( g + 12)
_2d _ 10 22n _ 220 _50z _ 50 _12g _ 144
25. 1(2 - y)
26. 0(a + 1) = 0
27. (-8 - s)(9)
28. 9(r – 1)
18. 0(x + 12)
_2 _ y _7a _7 11k _ 220 _9r _ 9_ 19 _r _ 27 53x _ 583 17n _ 17
37. PLANTS A planter weighs 2 pounds and holds 3 pounds of soil. Write two equivalent
expressions for the total weight of nine planters. Then find the weight.
9(2 + 3) = 9(5) = 45
OR 9(2) + 9(3) = 18 + 27
9(2 _ 3), 9(2) _ 9(3); 45 pounds
38. UNIFORMS A uniform costs \$42 for the sweater and \$29 for the slacks. Write two equivalent
expressions for the total cost of six uniforms. Then find the cost.
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