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. Prentice Hall Foundations Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 65 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
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