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: 32

Answer

$(2a-3b)(2a+3b)(4a^2+9b^2)$

Work Step by Step

RECALL: $x^2-y^2=(x-y)(x+y)$ The given expression can be written as: $(4a)^2-(9b^2)^2$ Factor this expression using the formula above with $x=4a^2$ and $y=9b^2$ to have: $=(4a^2-9b^2)(4a^2+9b^2) \\=[(2a)^2-(3b)^2](4a^2+9b^2)$ Factor the first binomial using the same formula with $x=2a$ and $y=3b$ to have: $=(2a-3b)(2a+3b)(4a^2+9b^2)$
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