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: 51

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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