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.4: 58

Answer

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

Work Step by Step

$$(2x-3)^3$$ $$=(2x-3)(2x-3)(2x-3)$$ $$=(2x-3)[(2x\times 2x)+(2x\times (-3))+(-3\times 2x)+(-3\times (-3))]$$ $$=(2x-3)(4x^2-6x-6x+9)$$ $$=(2x-3)(4x^2-12x+9)$$ $$=(2x\times 4x^2)+(2x\times (-12x))+(2x\times 9)+(-3\times 4x^2)+(-3\times (-12x))+(-3\times 9)$$ $$=8x^3-24x^2+18x-12x^2+36x-27$$ $$=8x^3-36x^2+54x-27$$
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