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: 13



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 $(5x-1)^3=\displaystyle \binom{3}{0}(5x)^3(-1)^0+\displaystyle \binom{3}{1}(5x^{2})(-1)^1 +\displaystyle \binom{3}{2}(5x)^1(-1)^2+\displaystyle \binom{3}{3}(5x)^0(-1)^3$ $=(125)(x^3)(1)+(3)(25x^2)(-1)+(3)(5x)(1)+(-1)(1)$ $\bf{(Simplify)}$ $=125x^3-75x^2+15x-1$
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