Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Prerequisites - P.3 - Polynomials and Special Products - Exercises - Page 31: 49

Answer

$8x^3-12x^2y+6xy^2-y^3$

Work Step by Step

Let's use the concept of cubing the binomial given by $$(x-y)^3=x^3-3x^2y+3xy^2-y^3$$ Hence, $\begin{align}(2x-y)^3&=(2x)^3-3(2x)^2(y)+3(2x)(y)^2-y^3\\&=8x^3-3y(4x^2)+6xy^2-y^3\\&=8x^3-12x^2y+6xy^2-y^3\end{align}$
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