8-7 Practice B ans

Name
8-7
Class
Date
Practice
Form K
Factoring Special Cases
Factor each expression.
1. c2 1 2c 1 1
2. d2 2 10d 1 25
(c 1 1)2
3. p2 2 24p 1 144
(d 2 5)2
4. w2 1 14w 1 49
(p 2 12)2
5. s2 1 16s 1 64
6. 9g2 1 24g 1 16
(s 1 8)2
(w 1 7)2
7. 25m2 2 60m 1 36
(5m 2 6)2
(3g 1 4)2
8. 4q2 2 32q 1 64
9. 49y2 2 84y 1 36
(7y 2 6)2
4(q 2 4)2
10. 121n2 2 66n 1 9
11. 81x2 2 18x 1 1
12. 100t2 2 100t 1 25
(9x 2 1)2
(11n 2 3)2
25(2t 2 1)2
The given expression represents the area. Find the side length of the square.
13.
14.
9w 2 4
6w 1 1
81w 2 Ľ 72w à 16
36w 2 à 12w à 1
15.
16.
11w 2 3
3w 2 8
9w 2 Ľ 48w à 64
121w 2 Ľ 66w à 9
17. Writing How can you tell that x2 2 19x 1 90 is not a perfect square
trinomial?
Sample: 90 is not a perfect square.
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Name
Class
8-7
Date
Practice (continued)
Form K
Factoring Special Cases
Factor each expression.
18. b2 2 121
(b 1 11)(b 2 11)
19. d2 2 81
(d 1 9)(d 2 9)
20. f 2 2 625
(f 1 25)(f 2 25)
21. 108x2 2 3
3(6x 1 1)(6x 2 1)
22. 50n2 2 8
2(5n 1 2)(5n 2 2)
23. 405z2 2 245
5(9z 1 7)(9z 2 7)
24. 216h2 2 150
6(6h 1 5)(6h 2 5)
25. 28y2 2 28
28(y 1 1)(y 2 1)
26. 50t2 1 40t 1 8
2(5t 1 2)(5t 1 2)
27. 12n2 2 36n 1 27
3(2n 2 3)(2n 2 3)
28. 180a2 2 300a 1 125
5(6a 2 5)(6a 2 5)
29. 250k2 2 200k 1 40
10(5k 2 2)(5k 2 2)
30. Writing Explain how to recognize a difference of two squares.
The expression is the difference of two terms that are both perfect squares.
31. a. Open-Ended Write an expression that shows the factored form of a
perfect-square trinomial.
Answers may vary. Sample: (5x 1 3)(5x 1 3) or (5x 1 3)2
b. Explain how you know your expression is a perfect-square trinomial when
expanded. It is in the form a2 1 2ab 1 b2 .
Mental Math For Exercises 32–34, find a pair of factors for each number by
using the difference of two squares.
32. 84 (14)(6)
33. 55 (11)(5)
34. 80 (20)(4)
35. Writing The area of a square painting is 225x4 1 240x2 1 64. Explain how
you would find a possible length of one side of the painting.
Since the trinomial is a perfect-square trinomial, the length of the
side could be a factor of the trinomial.
Prentice Hall Foundations Algebra 1 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
66