Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 11 - Section 11.4 - The Binomial Theorem - Exercise Set - Page 865: 37



Work Step by Step

Apply Binomial Theorem or Binomial expansion to find the first three terms of $(y^3-1)^{20}$. $(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$ Now, $(y^3-1)^{20}=\displaystyle \binom{20}{0}(y^3)^{20}(-1)^0+\displaystyle \binom{20}{1}(y^3)^{19}(-1)^1+\displaystyle \binom{20}{2}(y^3)^{18}(-1)^2$ Thus, $(y^3-1)^{20}=y^{60}-20y^{57}+190x^{54}$
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