Section 3.1 Simplifying Expressions and Combining Like Terms 139 For Exercises 13–16, identify the coefficients for each term. (See Example 1.) 13. 6p 4q 14. 5a3 2a 15. h 12 16. 8x 9 For Exercises 17–24, determine if the two terms are like terms or unlike terms. If they are unlike terms, explain why. (See Example 1.) 17. 3a, 2a 18. 8b, 12b 19. 4xy, 4y 20. 9hk, 9h 21. 14y2, 14y 22. 25x, 25x2 23. 17, 17y 24. 22t, 22 Concept 2: Commutative, Associative, and Distributive Properties For Exercises 25–32, apply the commutative property of addition or multiplication to rewrite each expression. (See Example 2.) 25. 5 w 26. t 2 27. r 122 28. a142 29. t 1s2 30. d1c2 31. p 7 32. q 8 For Exercises 33–40, apply the associative property of addition or multiplication to rewrite each expression. Then simplify the expression. (See Example 3.) 33. 3 18 t2 34. 7 15 p2 35. 216b2 36. 312c2 37. 316x2 38. 915k2 39. 9 112 h2 40. 11 14 s2 For Exercises 41–52, apply the distributive property. (See Examples 4 and 5.) 41. 41x 82 42. 513 w2 43. 41a 4b c2 44. 213q r s2 45. 21p 42 46. 61k 22 47. 13x 9 5y2 48. 1a 8b 4c2 49. 413 n22 50. 2113 t22 51. 315q 2s 3t2 52. 2110p 12q 32 For Exercises 53–60, apply the appropriate property to simplify the expression. 53. 612x2 54. 3112k2 55. 612 x2 56. 3112 k2 57. 8 14 p2 58. 3 125 m2 59. 814 p2 60. 3125 m2 Concept 3: Combining Like Terms For Exercises 61–72, combine the like terms. (See Examples 6 and 7.) 61. 6r 8r 62. 4x 21x 63. 4h 12h h 64. 9p 13p p 65. 4a2b 6a2b 66. 13xy2 8xy2 67. 10x 12y 4x 3y 9 68. 14a 5b 3a b 3 69. 8 6k 9k 12k 4 70. 5 11p 23p p 4 71. 8uv 6u 12uv 72. 9pq 9p 13pq Concept 4: Simplifying Expressions For Exercises 73–94, clear parentheses and combine like terms. (See Examples 8 and 9.) 73. 51t 62 2 74. 71a 42 8 75. 312x 12 13 76. 214b 32 10 77. 4 61y 32 78. 11 21p 82
miller_prealgebra_2e_ch1_3
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