Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Section 5.5 - Factoring Special Forms - Exercise Set - Page 372: 93

Answer

$(x-2y)(x^2-3xy+y^2)$

Work Step by Step

The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$. The formula for factoring the difference of two cubes is: $A^3-B^3=(A-B)(A^2+AB+B^2)$. Hence here: $(x-y)^3-y^3=\\=(x-y-y)((x-y)^2+(x-y)\cdot y+(y)^2)\\=(x-2y)(x^2-2xy+y^2+xy-y^2+y^2)\\=(x-2y)(x^2-3xy+y^2)$
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