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: 56

Answer

$x^3-3x^2+3x-1$

Work Step by Step

$$(x-1)^3$$ $$=(x-1)(x-1)(x-1)$$ $$=(x-1)[(x\times x)+(x\times (-1))+(-1\times x)+(-1\times (-1))]$$ $$=(x-1)(x^2-x-x+1)$$ $$=(x-1)(x^2-2x+1)$$ $$=(x\times x^2)+(x\times (-2x))+(x\times 1)+(-1\times x^2)+(-1\times (-2x))+(-1\times 1)$$ $$=x^3-2x^2+x-x^2+2x-1$$ $$=x^3-3x^2+3x-1$$
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