College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.5 - The Binomial Theorem - 9.5 Assess Your Understanding: 31

Answer

The coefficient of the term that contains $x^7$ is: $-101,376$

Work Step by Step

RECALL: The term containing $x^j$ in the expansion of $(x+c)^n$ is: ${n}\choose{n-j}$$c^{n-j}x^j$ Using the formula above, replacing $x$ with $2x$ and $c$ with $-1$, the term containing $x^7$ in the expansion of $(2x-1)^{12}$ is: =${12}\choose{12-7}$ $(-1)^{12-7}(2x)^7$ =${12}\choose{5}$ $(-1)^{5}(2x)^7$ $=\dfrac{12!}{5!7!}\cdot (-1) \cdot 128x^7 \\=792\cdot (-128x^7) \\=-101,376x^7$ Thus, the coefficient of the term that contains $x^7$ is $-101,376$.
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