By Cynthia Y. Young

The recent third version of Cynthia Young's *Algebra & Trigonometry* maintains to bridge the distance among in-class paintings and homework through assisting readers conquer universal studying obstacles and construct self belief of their skill to do mathematics. The textual content positive aspects really distinctive, robust pedagogy and is written in a transparent, unmarried voice that speaks on to scholars and mirrors how teachers converse in lectures. during this revision, younger allows readers to turn into self reliant, winning newbies via together with thousands of extra routines, extra possibilities to exploit expertise, and a brand new themed modeling venture that empowers them to use what they've got realized within the school room to the area outdoors the classroom. The seamlessly built-in electronic and print assets to accompany *Algebra & Trigonometry 3e *offer extra instruments to assist clients adventure good fortune.

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**Example text**

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. 2l ϩ 2w 72. x - m s for for l ϭ 5, w ϭ 10 x ϭ 100, m ϭ 70, s ϭ 15 A P P L I C AT I O N S On December 16, 2007, the United States debt was estimated at $9,176,366,494,947, and at that time the estimated population was 303,818,361 citizens.

A. 50 b. 1 20 d. Ϫ40 c. (Ϫ3)0 Solution: b. 1 1 = = 1 1 20 c. (Ϫ3)0 ϭ 1 d. Ϫ40 ϭ Ϫ1 { a. 50 ϭ 1 1 We now can evaluate expressions involving integer (positive, negative, or zero) exponents. What about when expressions involving integer exponents are multiplied, divided, or raised to a power? 23 # 24 = 2 # 2 # 2 # 2 # 2 # 2 # 2 = 23 + 4 = 27 5 2 = 23 When expressions with the same base are divided, the exponents are subtracted. u M ATH When expressions with the same base are multiplied, the exponents are added.

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). Solution: ᭤ ᭤ ᭤ 5x2(3x5 - x3 + 7x - 4) ᭤ Use the distributive property. ϭ 5x2(3x5) Ϫ 5x2(x3) ϩ 5x2(7x) Ϫ 5x2(4) Multiply each set of monomials. ■ Answer: 12x4 Ϫ 6x3 ϩ 3x2 ■ YO U R T U R N ϭ 15x7 Ϫ 5x5 ϩ 35x3 Ϫ 20x2 Find the product and simplify 3x2(4x2 Ϫ 2x ϩ 1).