College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5: 62

Answer

$(3x-1)(9x^{2}+3x+1)$

Work Step by Step

If $a$ and $b$ are real numbers, we know that $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$. Therefore, we know that $27x^{3}-1=(3x-1)((3x)^{2}+3x\times1+1^{2})=(3x-1)(9x^{2}+3x+1)$. In this case, $a=3x$ and $b=1$.
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