Algebra & Trigonometry by Cynthia Y. Young

By Cynthia Y. Young

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Solution (b): ➤ 2(y Ϫ 6) ϭ 2(y) Ϫ 2(6) Use the distributive property. ϭ 2y Ϫ 12 Perform the multiplication. ■ YO U R T U R N ■ Use the distributive property to eliminate the parentheses. a. 2(x ϩ 3) Answer: a. 2x ϩ 6 b. 5y Ϫ 15 b. 5(y Ϫ 3) You also probably know the rules that apply when multiplying a negative real number. ” P R O P E RTI E S O F N E GATIVE S MATH (LET a DESCRIPTION AND b BE POSITIVE REAL NUMBERS) EXAMPLE A negative quantity times a positive quantity is a negative quantity. (Ϫa)(b) ϭ Ϫab (Ϫ8)(3) ϭ Ϫ24 A negative quantity divided by a positive quantity is a negative quantity.

S. National Debt. Round the debt to the nearest million. 74. S. Population. Round the number of citizens to the nearest thousand. 75. S. Debt. If the debt is distributed evenly to all citizens, what is the national debt per citizen? Round your answer to the nearest dollar. 76. S. Debt. If the debt is distributed evenly to all citizens, what is the national debt per citizen? Round your answer to the nearest cent. 1 Real Numbers ■ 17 C AT C H T H E M I S TA K E In Exercises 77–80, explain the mistake that is made.

X Ϫ 5)2 Inner r Difference of two squares a. (x - 5)(x + 5) = x + 5x - 5x - 5 = 2 2 r r Outer Last s First r Solution: x2 - 52 = x2 - 25 Inner r r First b. (x + 5) = (x + 5)(x + 5) = x + 5x + 5x + 52 = x2 + 2(5x) + 52 = x2 + 10x + 25 2 2 r r Last Outer Inner r r First r r c. (x - 5)2 = (x - 5)(x - 5) = x2 - 5x - 5x + 52 = x2 - 2(5x) + 52 = x2 - 10x + 25 Outer Last Let a and b be any real number, variable, or algebraic expression in the following special products. Study Tip DIFFERENCE O F T W O S Q UAR E S (a ϩ b)(a Ϫ b) (a + b)(a - b) = a2 - b2 ϭ a2 Ϫ ab ϩ ab Ϫ b2 ϭ a2 Ϫ b2 P E R F E CT S Q UAR E S Square of a binomial sum: Square of a binomial difference: EXAMPLE 8 (a ϩ b)2 ϭ (a ϩ b)(a ϩ b) ϭ a2 ϩ 2ab ϩ b2 (a Ϫ b)2 ϭ (a Ϫ b)(a Ϫ b) ϭ a2 Ϫ 2ab ϩ b2 Finding the Square of a Binomial Sum Find (x ϩ 3)2.

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