Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - 5.3 - Multiplying Polynomials - Problem Set 5.3 - Page 208: 111



Work Step by Step

Using $(a-b)(a+b)=a^2-b^2$, or the product of the sum and difference of like terms, the given expression, $ -2x(4x+y)(4x-y) ,$ is equivalent to \begin{array}{l}\require{cancel} -2x[(4x)^2-(y)^2] \\\\= -2x(16x^2-y^2) .\end{array} Using the Distributive Property, the expression, $ -2x(16x^2-y^2) ,$ is equivalent to \begin{array}{l}\require{cancel} -32x^3+2xy^2 .\end{array}
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