Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Section 11.5 - The Binomial Theorem - Exercise Set - Page 664: 20

Answer

$x^6 + 18 x^5 y + 135 x^4 y^2 + 540 x^3 y^3 + 1215 x^2 y^4 + 1458 x y^5 + 729 y^6 $

Work Step by Step

Using the Binomial Formula, the expression $ (x+3y)^6 $ expands to \begin{array}{l} x^6(3y)^0+ \dfrac{6}{1!}x^5(3y)^1+ \dfrac{6\cdot5}{2!}x^4(3y)^2+ \dfrac{6\cdot5\cdot4}{3!}x^3(3y)^3+ \dfrac{6\cdot5\cdot4\cdot3}{4!}x^2(3y)^4+ \dfrac{6\cdot5\cdot4\cdot3\cdot2}{5!}x^1(3y)^5+ \dfrac{6\cdot5\cdot4\cdot3\cdot2\cdot1}{6!}x^0(3y)^6+ \\\\\\= x^6 + 18 x^5 y + 135 x^4 y^2 + 540 x^3 y^3 + 1215 x^2 y^4 + 1458 x y^5 + 729 y^6 \end{array}
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