College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.6 - Factoring - P.6 Exercises - Page 42: 41



Work Step by Step

RECALL: $A^3-B^3=(A-B)(A^2+AB+B^2)$ The given binomial can be written as: $=2^3a^3-1^3 \\=(2a)^3-1^3$ The binomial above is a difference of two cubes. Factor using the the formula above with $A=2a$ and $B=1$ to obtain: $=(2a-1)[(2a)^2+(2a)(1) + 1^2) \\=(2a-1)(4a^2+2a+1)$
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