Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.5 - The Binomial Theorum - Exercise Set - Page 1092: 14



Work Step by Step

Binomial Theorem or Binomial expansion can be defined as: $(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$ Need to apply the formula to get the Binomial Expansion. we have $(4x-1)^3=\displaystyle \binom{3}{0}(4x)^3(-1)^0+\displaystyle \binom{3}{1}(4x^{2})(-1)^1 +\displaystyle \binom{3}{2}(4x)^1(-1)^2+\displaystyle \binom{3}{3}(4x)^0(-1)^3$ $=(64)(x^3)(1)+3(16x^2)(-1)+(3)(4x)(1)+(-1)(1)$ $\bf{(Simplify)}$ $=64x^3-48x^2+12x-1$
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