Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Chapters R-5 - Cumulative Review Exercises: 30

Answer

$(2p +3 )(4p^2-6p +9 )$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ 8p^3+27 ,$ use the factoring of the sum of $2$ cubes. $\bf{\text{Solution Details:}}$ The expressions $ 8p^3 $ and $ 27 $ are both perfect cubes (the cube root is exact). Hence, $ 8p^3+27 ,$ is a sum of $2$ cubes. Using the factoring of the sum of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (2p )^3+(3 )^3 \\\\= (2p +3 )[(2p )^2-2p (3 )+(3 )^2] \\\\= (2p +3 )(4p^2-6p +9 ) .\end{array}
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