Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.2 Factoring - R.2 Exercises: 29

Answer

$(3r-4s)(9r^2+12rs+16s^2)$

Work Step by Step

RECALL: $a^3-b^3 = (a-b)(a^2+ab+b^2)$ Write $27r^3$ and $64s^3$ as cubes to have: $(3r)^3-(4s)^3$ Factor the difference of two cubes using the formula above with $a=3r$ and $b=4s$ to have: $=(3r-4s)[(3r)^2+(3r)(4s) + (4s)^2] \\=(3r-4s)(9r^2+12rs+16s^2)$
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