Math 40
Prealgebra
Section 3.4 - HOMEWORK
In Exercises 1-16, combine like terms by first using the distributive property to factor
out the common variable part, and then simplifying.
1.
17xy2 + 18xy2 + 20xy2
2.
13xy − 3xy + xy
3.
−8xy2 − 3xy2 − 10xy2
4.
−12xy − 2xy + 10xy
5.
4xy − 20xy
6.
−7y 3 + 15y3
7.
12r − 12r
8.
16s − 5s
9.
−11x − 13x + 8x
10. −9r − 10r + 3r
11. −5q + 7q
12. 17n + 15n
13. r − 13r − 7r
14. 19m + m + 15m
15. 3x3 − 18x3
16. 3x2 y + 2x2 y
In Exercises 17-32, combine like terms by first rearranging the terms, then
using the distributive property to factor out the common variable part, and then
simplifying.
17. −8 + 17n + 10 + 8n
18. 11 + 16s − 14 − 6s
19. −2x3 − 19x2 y − 15x2 y + 11x3
20. −9x2 y − 10y3 − 10y 3 + 17x2y
21. −14xy − 2x3 − 2x3 − 4xy
22. −4x3 + 12xy + 4xy − 12x3
23. −13 + 16m + m + 16
24. 9 − 11x − 8x + 15
25. −14x2 y − 2xy2 + 8x2 y + 18xy2
26. −19y2 + 18y3 − 5y 2 − 17y 3
27. −14x3 + 16xy + 5x3 + 8xy
28. −16xy + 16y2 + 7xy + 17y 2
29. 9n + 10 + 7 + 15n
30. −12r + 5 + 17 + 17r
31. 3y + 1 + 6y + 3
32. 19p + 6 + 8p + 13
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2015 Worrel
Math 40
Prealgebra
Section 3.4 - HOMEWORK
In Exercises 33-56, simplify the expression by first using the distributive property
to expand the expression, and then rearranging and combining like terms mentally.
33. −4(9x2y + 8) + 6(10x2y − 6)
34. −4(−4xy + 5y 3) + 6(−5xy − 9y 3)
35. 3(−4x2 + 10y2 ) + 10(4y2 − x2 )
36. −7(−7x3 + 6x2 ) − 7(−10x2 − 7x3 )
37. −s + 7 − (−1 − 3s)
38. 10y − 6 − (−10 − 10y)
39. −10q − 10 − (−3q + 5)
40. −2n + 10 − (7n − 1)
41. 7(8y + 7) − 6(8 − 7y)
42. −6(−5n − 4) − 9(3 + 4n)
43. 7(10x2 − 8xy2 ) − 7(9xy2 + 9x2 )
44. 10(8x2 y − 10xy2) + 3(8xy2 + 2x2 y)
45. −2(6 + 4n) + 4(−n − 7)
46. −6(−2 − 6m) + 5(−9m + 7)
47. 8 − (4 + 8y)
48. −1 − (8 + s)
49. −8(−n + 4) − 10(−4n + 3)
50. 3(8r − 7) − 3(2r − 2)
51. −5 − (10p + 5)
52. −1 − (2p − 8)
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2015 Worrel
Math 40
Prealgebra
Section 3.4 - HOMEWORK
53. 7(1 + 7r) + 2(4 − 5r)
54. (5 − s) + 10(9 + 5s)
55. −2(−5 − 8x2 ) − 6(6)
56. 8(10y 2 + 3x3 ) − 5(−7y2 − 7x3 )
57. The length of a rectangle, L, is 2 feet longer than 6 times its width, W. Find the perimeter
of the rectangle in terms of its width alone.
58. The length of a rectangle, L, is 7 feet longer than 6 times its width, W. Find the perimeter
of the rectangle in terms of its width alone.
59. The width of a rectangle, W, is 8 feet shorter than its length, L. Find the perimeter of the
rectangle in terms of its length alone.
60. The width of a rectangle, W, is 9 feet shorter than its length, L. Find the perimeter of the
rectangle in terms of its length alone.
61. The length of a rectangle, L, is 9 feet shorter than 4 times its width, W. Find the perimeter
of the rectangle in terms of its width alone.
62. The length of a rectangle, L, is 2 feet shorter than 6 times its width, W. Find the perimeter
of the rectangle in terms of its width alone.
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2015 Worrel