Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8-8
DATE
PERIOD
NAME
DATE
8-8
Skills Practice
Practice
Differences of Squares
Differences of Squares
Factor each polynomial, if possible. If the polynomial cannot be factored, write
prime.
Factor each polynomial, if possible. If the polynomial cannot be factored,
write prime.
1. a2 - 4
1. k2 - 100
2. n2 - 64
(a + 2)(a - 2)
2. 81 - r2
(k + 10)(k - 10)
(n + 8)(n - 8)
4. 4x + 25
4. -16 + p2
(1 + 7d)(1 - 7d)
5. 144 - 9f
2
7. 121m - 144p
5. k2 + 25
(6 - 10w)(6 + 10w)
prime
2
8. 32 - 8y
(11m - 12p)(11m + 12p)
6. 36 - 100w2
2
10. 32t - 18u
2
(t + 9u)(t - 9u)
3
13. 45q - 20q
(2h + 5g)(2h - 5g)
9. 64m2 - 9y2
prime
8(x + 3p)(x - 3p)
14. 32a2 - 50b2
5(2q + r)(2q - r)
2(4a + 5b)(4a - 5b)
Solve each equation by factoring. Check the solutions.
3
±−
$
15. 16x2 - 9 = 0
4
7
±−
$
17. 36q2 - 49 = 0
6
1
±−
$
Glencoe Algebra 1
3
±−
5
$
1 2
23. −
h - 16 = 0 {±20}
Chapter 8
5
9
±−
$
18. 81 - 4b2 = 0
20. 18a2 = 8
2
4
±−
$
16. 25p2 - 16 = 0
2
2
±−
$
49
22. k2 - −
=0
64
3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. 20q2 - 5r2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A25
12. 8x2 - 72p2
(2t + 7r)(2t - 7r)
25
6(2a - 3b)(2a + 3b)
12. 36z3 - 9z
9z (2z + 1)(2z - 1)
prime
3
14. 100b - 36b
4b(5b + 3)(5b - 3)
15. 3t4 - 48t2
3t 2(t + 4)(t - 4)
Solve each equation by factoring. Check your solutions.
16. 4y2 = 81
11. -49r2 + 4t2
9
21. n2 - −
=0
25
9. 24a2 - 54b2
8(2 - y)(2 + y)
11. 9d - 32
5q(3q + 2)(3q - 2)
(6g + 7h)(6g - 7h)
10. 4c2 - 5d2
(8m - 3y)(8m + 3y)
19. 16d2 = 4
2
17. 64p2 = 9
9
±−
2
$
19. 32 - 162k2 = 0
5
±−
$
$
7
64
20. t2 - −
=0
16
21. −
- v2 = 0
8
±−
$
4
±−
$
121
4
±−
$
9
1 2
22. −
x - 25 = 0
36
18. 98b2 - 50 = 0
3
±−
8
7
11
3
23. 27h = 48h
4
±−
, 0$
{±30}
49
3
24. 75g = 147g
7
±−
, 0$
5
3
25. EROSION A rock breaks loose from a cliff and plunges toward the ground 400 feet
below. The distance d that the rock falls in t seconds is given by the equation d = 16t2.
How long does it take for the rock to hit the ground? 5 s
26. FORENSICS Mr. Cooper contested a speeding ticket given to him after he applied his
brakes and skidded to a halt to avoid hitting another car. In traffic court, he argued that
the length of the skid marks on the pavement, 150 feet, proved that he was driving
under the posted speed limit of 65 miles per hour. The ticket cited his speed at 70 miles
1 2
per hour. Use the formula −
s = d, where s is the speed of the car and d is the length of
7
±−
$
24
the skid marks, to determine Mr. Cooper’s speed when he applied the brakes. Was Mr.
Cooper correct in claiming that he was not speeding when he applied the brakes?
8
60 mph; yes
1 2
24. −
y = 81 {±36}
16
52
Answers
Glencoe Algebra 1
Chapter 8
53
Glencoe Algebra 1
Answers (Lesson 8-8)
8. 4h2 - 25g2
(4p + 6)(4p - 6)
6. 36g2 - 49h2
2
2(4t - 3u)(4t + 3u)
7. t2 - 81u2
2
(12 + 3f )(12 - 3f )
prime
(p + 4)(p - 4)
3. 16p2 - 36
(9 + r)(9 - r )
2
3. 1 - 49d2
PERIOD
Lesson 8-8
Chapter 8
NAME