College Algebra (10th Edition)

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

Chapter R - Section R.5 - Polynomials - R.4 Assess Your Understanding: 90

Answer

$27x^3-54x^2+36x-8$

Work Step by Step

RECALL: The formula for the cube of a binomial $a-b$ is $(a-b)^3=a^3-3a^2b+3ab^2-b^3$ Use the formula above with $a=3x$ and $b=2$ to obtain: $(3x-2)^3 \\= (3x)^3 - 3(3x)^2(2) + 3(3x)(2^2) - 2^3 \\=27x^3 - 3(9x^2)(2)+3(3x)(4)-8 \\=27x^3-54x^2+36x-8$
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