Copyright © 2013 Pearson Education, Inc. Section 5.4 Special Products

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Example Multiply. a. (x + 4)(x – 4)b. (3t + 4s)(3t – 4s) Solution a. We can apply the formula for the product of a sum and difference. b. (x + 4)(x – 4)= (x) 2 − (4) 2 = x 2 − 16 (3t + 4s)(3t – 4s) = (3t) 2 – (4s) 2 = 9t 2 – 16s 2 Page 325

Problem 10, 18 Page 329

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Example Multiply. a. (x + 7) 2 b. (4 – 3x) 2 Solution a. We can apply the formula for squaring a binomial. b. (x + 7) 2 = (x) 2 + 2(x)(7) + (7) 2 = x x + 49 (4 – 3x) 2 = (4) 2 − 2(4)(3x) + (3x) 2 = 16 − 24x + 9x 2

Problem 30, 38 Page 329

Problem 56, 62 modified Page 330

DONE

Objectives Product of a Sum and Difference Squaring Binomials Cubing Binomials

Example Use the product of a sum and difference to find 31 ∙ 29. Solution Because 31 = and 29 = 30 – 1, rewrite and evaluate 31 ∙ 29 as follows. 31 ∙ 29= (30 + 1)(30 – 1) = 30 2 – 1 2 = 900 – 1 = 899

Example Multiply (5x – 3) 3. Solution = (5x − 3)(5x − 3) 2 = 125x 3 (5x – 3) 3 = (5x − 3)(25x 2 − 30x + 9) = 125x 3 – 225x x – 27 – 27– 150x x– 75x x

Example If a savings account pays x percent annual interest, where x is expressed as a decimal, then after 2 years a sum of money will grow by a factor of (x + 1) 2. a.Multiply the expression. b.Evaluate the expression for x = 0.12 (or 12%), and interpret the result. Solution a. (1 + x) 2 = 1 + 2x + x 2 b. Let x = (0.12) + (0.12) 2 = The sum of money will increase by a factor of For example if $5000 was deposited in the account, the investment would grow to $6272 after 2 years.