NAME
DATE
8-5
PERIOD
Practice
Using the Distributive Property
Factor each polynomial.
2. 4d2 + 16
1. 64 - 40ab
3. 6r2t - 3rt2
8(8 - 5ab)
2
4(d + 4)
3rt(2r - t)
4. 15ad + 30a2d2
5. 32a2 + 24b2
6. 36xy2 - 48x2y
15ad(1 + 2ad)
7. 30x3y + 35x2y2
2
5x y(6x + 7y)
10. 8p2r2 - 24pr3 + 16pr
2
8pr(pr - 3r + 2)
13. x2 + 4x + 2x + 8
(x + 2)(x + 4)
16. 6xy - 8x + 15y - 20
(2x + 5)(3y - 4)
8(4a2 + 3b2)
12xy(3y - 4x)
8. 9a3d2 - 6ad3
2
9. 75b2g3 + 60bg3
2
3ad (3a - 2d)
15bg3(5b + 4)
11. 5x3y2 + 10x2y + 25x
12. 9ax3 + 18bx2 + 24cx
2 2
3x(3ax2 + 6bx + 8c)
5x(x y + 2xy + 5)
14. 2a2 + 3a + 6a + 9
15. 4b2 - 12b + 2b - 6
(a + 3)(2a + 3)
(4b + 2)(b - 3)
18. 12a2 - 15ab - 16a + 20b
17. -6mp + 4m + 18p - 12
(-2m + 6)(3p - 2)
(3a - 4)(4a - 5b)
Solve each equation. Check your solutions.
19. x(x - 32) = 0
{0, 32}
-6, −73 25. 2z2 + 20z = 0
{-10, 0}
21. (y - 3)(y + 2) = 0
{-4, 0}
{-2, 3}
23. (2y + 5)(y - 4) = 0
24. (4y + 8)(3y - 4) = 0
- −52 , 4
-2, −43 26. 8p2 - 4p = 0
27. 9x2 = 27x
0, −12 {0, 3}
28. 18x2 = 15x
29. 14x2 = -21x
0, −56 - −32 , 0
30. 8x2 = -26x
13
, 0
- −
4
31. LANDSCAPING A landscaping company has been commissioned to design a triangular
flower bed for a mall entrance. The final dimensions of the flower bed have not been
determined, but the company knows that the height will be two feet less than the base.
1 2
b - b.
The area of the flower bed can be represented by the equation A = −
(
)
1
a. Write this equation in factored form. A = b − b - 1
2
2
b. Suppose the base of the flower bed is 16 feet. What will be its area? 112 ft2
32. PHYSICAL SCIENCE Mr. Alim’s science class launched a toy rocket from ground level
with an initial upward velocity of 60 feet per second. The height h of the rocket in feet
above the ground after t seconds is modeled by the equation h = 60t - 16t2. How long
was the rocket in the air before it returned to the ground? 3.75 s
Chapter 8
34
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
22. (a + 6)(3a - 7) = 0
20. 4b(b + 4) = 0