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 - Page 65: 101



Work Step by Step

The least exponent of the binomials is $-3/2$. The numerical coefficients have a greatest factor of $2$. Factor out $2(3x+1)^{-3/2}$ to obtain: $=2(3x+1)^{-3/2}[1+2(3x+1)+3(3x+1)^{2}] \\=2(3x+1)^{-3/2}[1+6x+2+(3x+1)^{2}] \\=2(3x+1)^{-3/2}[6x+3+(3x+1)^{2}]$ Square the binomial to obtain: $\\=2(3x+1)^{-3/2}[6x+3+3(9x^2+6x+1)]$ Distribute $3$ then combine like terms to obtain: $=2(3x+1)^{-3/2}(6x+3+27x^2+18x+3) \\=2(3x+1)^{-3/2}(27x^2+24x+6)$ Factor out $3$ in the trinomial to obtain: $\\=2(3x+1)^{-3/2}\cdot 3(9x^2+8x+2) \\=\color{blue}{6(3x+1)^{-3/2}(9x^2+8x+2)}$
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