Question 118727

{{{(x-y)(x^2-xy+y^2)}}} Start with the given expression




{{{x(x^2-xy+y^2)-y(x^2-xy+y^2)}}} Expand the expression. Remember for something like {{{(a+b)(c+d+e)}}} it expands to {{{a(c+d+e)+b(c+d+e)}}}



{{{(x)*(1x^2)+(x)*(-1xy)+(x)*(1y^2)+(-y)*(1x^2)+(-y)*(-1xy)+(-y)*(1y^2)}}} Distribute



{{{x^3-x^2y+xy^2-yx^2+y^2x-y^3}}} Multiply



{{{-y^3+2xy^2-2x^2y+x^3}}} Combine like terms




{{{x^3-2x^2y+2xy^2-y^3}}} Rearrange the terms




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


In other words, {{{(x-y)(x^2-xy+y^2)=x^3-2x^2y+2xy^2-y^3}}}