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:
$...=x^{3}-2x^{2}y-4x^{2}y+8xy^{2}+4xy^{2}-8y^{3}=...$
$...=x^{3}-6x^{2}y+12xy^{2}-8y^{3}$
