Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - 11.4 The Binomial Theorem - 11.4 Exercises: 31

Answer

$x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6$

Work Step by Step

$(x+y)^n=\binom{n}{0}x^ny^0+\binom{n}{1}x^{n-1}y^1+...+\binom{n}{a}x^{n-a}y^a+..\binom{n}{n}x^{0}y^n$ Here: $n=6$, $(x+y)^6=\binom{6}{0}x^6y^0+\binom{6}{1}x^{6-1}y^1+\binom{6}{2}x^{6-2}y^2+\binom{6}{3}x^{6-3}y^3+\binom{6}{4}x^{6-4}y^4+\binom{6}{5}x^{6-5}y^5+\binom{6}{6}x^{6-6}y^6=$ $x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6$
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