By Cynthia Y. Young

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6x 7x 12 20 55. 3 7 + 40 24 56. -3 -7 - a b 10 12 60. 4 7 , 5 10 In Exercises 57–68, perform the indicated operation and simplify, if possible. 57. 2 # 14 7 3 61. 4b a , 9 27 65. 3x 9 , 4 16y a Z 0 y Z 0 58. 2# 9 3 10 62. 3a b , 7 21 66. 14m # 4 2 7 b Z 0 59. 2 10 , 7 3 63. 3x 6x , 10 15 x Z 0 64. 4 1 1 , 7 5 20 67. 3y 6x , 7 28 y Z 0 68. 2 1# 5 7 3 6 In Exercises 69–72, evaluate the algebraic expression for the speciﬁed values. 69. 71. ■ -c 2d for c ϭ Ϫ4, d ϭ 3 m1 # m2 r 2 for m1 ϭ 3, m2 ϭ 4, r ϭ 10 70.

CORRECT INCORRECT Eliminate the parentheses. ERROR: 3x3 Ϫ 2x ϩ 1 Ϫ x2 Ϫ 5x ϩ 9 3x3 Ϫ 2x ϩ 1 Ϫ x2 ϩ 5x Ϫ 9 Don’t forget to distribute the negative through the entire second polynomial. Identify like terms. Study Tip When subtracting polynomials, it is important to distribute the negative through all of the terms in the second polynomial. ■ Answer: x3 Ϫ 7x2 Ϫ 4x ϩ 3 3x - 2x + 1 - x - 5x + 9 3 2 Combine like terms. 2). 1). EXAMPLE 4 Multiplying a Monomial and a Polynomial Find the product and simplify 5x2(3x5 - x3 + 7x - 4).

The following ﬁgure and table illustrate the subset relationship and examples of different types of real numbers. Real Numbers Irrational Numbers Rational Numbers Integers Negative Counting Numbers NAME Every real number is either a rational number or an irrational number. Whole Numbers Zero SYMBOL Study Tip Fractions • Ratio of two nonzero integers, and • Does not reduce to an integer Natural Numbers D ESCRIPTION E XAMPLES N Natural numbers Counting numbers 1, 2, 3, 4, 5, . . W Whole numbers Natural numbers and zero 0, 1, 2, 3, 4, 5, .