Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.1 Polynomials - R.1 Exercises: 25

Answer

$(x-2y)^{3}=x^{3}-6x^{2}y+12xy^{2}-8y^{3}$

Work Step by Step

$(x-2y)^{3}$ Rewrite this expression as $(x-2y)(x-2y)(x-2y)$: $(x-2y)^{3}=(x-2y)(x-2y)(x-2y)=...$ First, evaluate $(x-2y)(x-2y)$ and simplify: $...=(x^{2}-2xy-2xy+4y^{2})(x-2y)=...$ $...=(x^{2}-4xy+4y^{2})(x-2y)=...$ Finally, evaluate $(x^{2}-4xy+4y^{2})(x-2y)$ and simplify again: $...=x^{3}-2x^{2}y-4x^{2}y+8xy^{2}+4xy^{2}-8y^{3}=...$ $...=x^{3}-6x^{2}y+12xy^{2}-8y^{3}$
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