Precalculus (6th Edition)

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

Chapter R - Review of Basic Concepts - R.6 Rational Exponents - R.6 Exercises: 100

Answer

$\color{blue}{3(3r+1)^{-2/3}(3r^2+3r+1)}$

Work Step by Step

The least exponent of the binomials is $-2/3$. Factor out $(3r+1)^{-2/3}$ to obtain: $=(3r+1)^{-2/3}[1+(3r+1)+(3r+1)^{2}] \\=(3r+1)^{-2/3}[3r+2+(3r+1)^{2}]$ Square the binomial then combine like terms to obtain: $=(3r+1)^{-2/3}(3r+2+9r^2+6r+1) \\=(3r+1)^{-2/3}(9r^2+9r+3)$ Factor out $3$ in the trinomial to obtain: $\\=\color{blue}{3(3r+1)^{-2/3}(3r^2+3r+1)}$
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