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: 38

Answer

$729 r^6 + 1458 r^5 s + 1215 r^4 s^2 + 540 r^3 s^3 + 135 r^2 s^4 + 18 r s^5 + s^6$

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: $n=6$, $x=3r$, $y=s$ $(3r+s)^6=\binom{6}{0}(3r)^{6}s^0+\binom{6}{1}(3r)^{6-1}s^1+\binom{6}{2}(3r)^{6-2}s^2+\binom{6}{3}(3r)^{6-3}s^3+\binom{6}{4}(3r)^{6-4}s^4+\binom{6}{5}(3r)^{6-5}s^5+\binom{6}{6}(3r)^{6-6}s^6=$ $729 r^6 + 1458 r^5 s + 1215 r^4 s^2 + 540 r^3 s^3 + 135 r^2 s^4 + 18 r s^5 + s^6$
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