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: 16



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 $(3x+1)^4=\displaystyle \binom{4}{0}(3x)^4(1)^0+\displaystyle \binom{4}{1}(3x)^3(1)^1+\displaystyle \binom{4}{2}(3x)^2(1)^2+\displaystyle \binom{4}{3}(3x)^1(1)^3+\displaystyle \binom{4}{4}(3x)^0(1)^3$ $=81x^4(1)+(4)(27x^3)(1)+(6)(9x^2)+12x+1(1)$$\bf{(Simplify)}$ $=81x^4+108x^3+54x^2+12x+1$
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