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: 17

Answer

$a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7$

Work Step by Step

Using the Binomial Formula, the expression $ (a+b)^7 $ expands to \begin{array}{l} a^7b^0+ \dfrac{7}{1!}a^6b^1+ \dfrac{7\cdot6}{2!}a^5b^2+ \dfrac{7\cdot6\cdot5}{3!}a^4b^3+\\ \dfrac{7\cdot6\cdot5\cdot4}{4!}a^3b^4+ \dfrac{7\cdot6\cdot5\cdot4\cdot3}{5!}a^2b^5+ \dfrac{7\cdot6\cdot5\cdot4\cdot3\cdot2}{6!}a^1b^6+\\ \dfrac{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{7!}a^0b^7 \\\\= a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7 \end{array}
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