College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.6 - The Binomial Theorem - 8.6 Exercises: 47

Answer

$3x^{2}+3xh+h^{2}$

Work Step by Step

We apply the binomial theorem to expand $(x+h)^3$: $(x+h)^3=x^{3}+3x^{2}h^1+3x^1h^{2}+h^{3}$ Now we simplify: $\displaystyle \frac{(x+h)^{3}-x^{3}}{h}=\frac{x^{3}+3x^{2}h+3xh^{2}+h^{3}-x^{3}}{h}=\frac{3x^{2}h+3xh^{2}+h^{3}}{h}=\frac{h(3x^{2}+3xh+h^{2})}{h}=3x^{2}+3xh+h^{2}$
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