Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.5 - Multiplying Polynomials - Exercise Set: 95

Answer

Answer : (a)= ${a^2} - {b^2}$ (b)= $4{x^2} - 9{y^2}$ (c)= $16{x^2} - 49$ (d)= General Statement: ${x^2} -{y^2}$

Work Step by Step

Steps: [A] =(a+b)(a-b) =a(a) - a(b) + a(b) -b(b) =${a^2} -ab +ab - {b^2}$ = ${a^2} - {b^2}$ [B] =(2x + 3y)(2x - 3y) =2x(2x) - 2x(3y) + 2x(3y) - 3y(3y) =$4{x^2} - 6xy +6xy - 9{y^2}$ = $4{x^2} - 9{y^2}$ [C] =(4x+7)(4x-7) =4x(4x) - 4x(7) + 4x(7) - 7(7) =$16{x^2} - 28x + 28x - 49$ = $16{x^2} - 49$ [D] General Statement: (x+y)(x-y) = ${x^2} - {y^2}$ Proof: (x+y)(x-y) =${x^2} - x(y) + x(y)- {y^2}$ =${x^2} - {y^2}.$
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