Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Section 5.2 - Multiplication of Polynomials - Exercise Set - Page 338: 68

Answer

$9a^{2n}-6a^nb^n+b^{2n}$

Work Step by Step

The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$. The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$. Hence here: $(3a^n-b^n)^2=(3a^n)^2-2\cdot3a^n\cdot b^n+(b^n)^2=9a^{2n}-6a^nb^n+b^{2n}$
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