Calculus with Applications (10th Edition)

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

Chapter R - Algebra Reference - R.6 Exponents - R.6 Exercises - Page R-25: 51



Work Step by Step

$3x^{3}(x^{2}+3x)^{2}-15x(x^{2}+3x)^{2}$ ... factor x out of $x^{2}+3x$ $= 3x^{3}[x\cdot(x+3)]^{2}-15x[x\cdot(x+3)]^{2}$ ....... apply $(ab)^{m}=a^{m} b^{m}$ on $[x\cdot(x+3)]^{2}$ $= 3x^{3}\cdot x^{2}\cdot(x+3)^{2}-15x\cdot x^{2}\cdot(x+3)^{2}$ $= 3x^{5}\cdot(x+3)^{2}-15x^{3}\cdot(x+3)^{2}$ greatest common factor=$3x^{3}(x+3)^{2}$ $= x^{2}\cdot[3x^{3}(x+3)^{2}]-5\cdot[3x^{3}(x+3)^{2}]$ factor out the term $[3x^{3}(x+3)^{2}]$ $=3x^{3}(x+3)^{2}(x^{2}-5)$
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