Algebra by Moh T.T.

By Moh T.T.

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We call the variables in a term literal factors, and we call the numerical factor the numerical coefficient. Thus in 7xy, the x and y are literal factors, and 7 is the numerical coefficient. The numerical coefficient of the term Ϫ4abc is Ϫ4. Since z ϭ 1(z), the numerical coefficient of the term z is 1. Terms that have the same literal factors are called like terms or similar terms. Some examples of similar terms are 3x and 9x 14abc and 29abc 7xy and Ϫ15xy 4z, 9z, and Ϫ14z We can simplify algebraic expressions that contain similar terms by using a form of the distributive property.

2)(Ϫ71)(50) 19. (4) (Ϫ16)(Ϫ9)(Ϫ25) 20. (Ϫ2)(18)(Ϫ12)(Ϫ5) 21. 37(Ϫ42 Ϫ58) 22. Ϫ46(Ϫ73 Ϫ 27) 23. 59(36) ϩ 59(64) 24. Ϫ49(72) Ϫ 49(28) 25. 15(Ϫ14) ϩ 16(Ϫ8) 26. Ϫ9(14) Ϫ 7(Ϫ16) 27. 17 ϩ (Ϫ18) Ϫ 19 Ϫ 14 ϩ 13 Ϫ 17 57. 3(a Ϫ 1) Ϫ 2(a Ϫ 6) ϩ 4(a ϩ 5) 58. Ϫ4(a ϩ 2) ϩ 6(a ϩ 8) Ϫ 3(a Ϫ 6) 59. Ϫ2(m ϩ 3) Ϫ 3(m Ϫ 1) ϩ 8(m ϩ 4) 60. 5(m Ϫ 10) ϩ 6(m Ϫ 11) Ϫ 9(m Ϫ 12) 61. (y ϩ 3) Ϫ (y Ϫ 2) Ϫ (y ϩ 6) Ϫ 7(y Ϫ 1) 62. Ϫ(y Ϫ 2) Ϫ (y ϩ 4) Ϫ (y ϩ 7) Ϫ 2(y ϩ 3) For Problems 63–80, simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables.

8) (Ϫ7) ϩ (Ϫ6) Ϫ (9)(12) 19. Express 360 as a product of prime factors. 7. 6(Ϫ4) Ϫ (Ϫ8)(Ϫ5 Ϫ16 8. Ϫ14 ϩ 23 Ϫ 17 Ϫ 19 ϩ 26 9. (Ϫ14) (4) Ϭ 4 ϩ (Ϫ6) 20. Find the greatest common factor of 36, 60, and 84. 21. Find the least common multiple of 9 and 24. 22. State the property of integers demonstrated by [Ϫ3 ϩ (Ϫ4)] ϩ (Ϫ6) ϭ Ϫ3 ϩ [(Ϫ4) ϩ (Ϫ6)]. 10. 6(Ϫ9) Ϫ (Ϫ8) Ϫ (Ϫ7)(4) ϩ 11 23. State the property of integers demonstrated by 8(25 ϩ 37) ϭ 8(25) ϩ 8(37). 11. It was reported on the 5 o’clock news that the current temperature was 7°F.

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