Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - Chapter 5 Review Problem Set: 38

Answer

$a^{3}$ - 18$a^{2}$ + 108a - 216

Work Step by Step

$(a-6)^{3}$ = (a-6)(a-6)(a-6) = (a-6)(a-6) $\times$ (a-6) = ($a^{2}$ - 2$\times$a$\times$6 + $6^{2}$) $\times$ (a-6) = ($a^{2}$ - 12a + 36) $\times$ (a - 6) = RECALL: The distributive property states that for any real numbers a, b, and c: a(b+c)=ab+ac a(b−c)=ab−ac Use the distributive property (which is shown above) to obtain: a($a^{2}$ - 12a + 36) - 6($a^{2}$ - 12a + 36) = $a^{3}$ - 12$a^{2}$ + 36a - 6$a^{2}$ + 72a - 216 = Simplify. $a^{3}$ - 18$a^{2}$ + 108a - 216
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