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: 77

Answer

$x^3-y^3$

Work Step by Step

$$(x-y)(x^2+xy+y^2)$$ To multiply a binomial by a trinomial, multiply each term in the binomial by each term in the trinomial: $$=(x\times x^2)+(x\times xy)+(x\times y^2)+(-y\times x^2)+(-y\times xy)+(-y\times y^2)$$ $$=x^3+x^2y+xy^2-x^2y-xy^2-y^3$$ Combine like terms: $$=x^3-y^3$$
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