Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 3 - Exponents, Polynomials and Functions - 3.5 Special Factoring Techniques - 3.5 Exercises: 32

Answer

$(9m^2+4p^2)(3m+2p)(3m-2p)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ 81m^4-16p^4 ,$ use the factoring of the difference of $2$ squares. $\bf{\text{Solution Details:}}$ The expressions $ 81m^4 $ and $ 16p^4 $ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $ 81m^4-16p^4 ,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares, which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (9m^2)^2-(4p^2)^2 \\\\= (9m^2+4p^2)(9m^2-4p^2) .\end{array} The expressions $ 9m^2 $ and $ 4p^2 $ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $ 9m^2-4p^2 ,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares, which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (9m^2+4p^2)[(3m)^2-(2p)^2] \\\\= (9m^2+4p^2)(3m+2p)(3m-2p) .\end{array}
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