Question 600633
{{{(x-2y)^3}}}


{{{(x-2y)(x-2y)(x-2y)}}}


{{{(x-2y)(x^2-2xy-2xy+4y^2)}}}


{{{(x-2y)(x^2-4xy+4y^2)}}}


{{{x(x^2-4xy+4y^2)-2y(x^2-4xy+4y^2)}}}


{{{x^3-4x^2y+4xy^2-2x^2y+8xy^2-8y^3}}}


{{{x^3-6x^2y+12xy^2-8y^3}}}


So {{{(x-2y)^3}}} expands and simplifies to {{{x^3-6x^2y+12xy^2-8y^3}}}


In other words, {{{(x-2y)^3=x^3-6x^2y+12xy^2-8y^3}}} for all values of x and y.