Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises - Page 44: 79



Work Step by Step

With $216=6^3$, the given polynomial is equivalent to: $=(r+6)^3-6^3$ Factor using the formula $a^3-b^3=(a-b)(a^2+ab+b^2)$ with $a=r+6$ and $b=6$ to obtain: $=(r+6-6)[(r+6)^2+(r+6)(6) + 6^2] \\=(r+0)[(r^2+12r+36)+6r+36+36] \\=r(r^2+12r+36+6r+72) \\=\color{blue}{r(r^2+18r+108)}$
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