How to prove $x^3-y^3 = (x-y)(x^2+xy+y^2)$ without expand the right side? I can prove that $x^3-y^3 = (x-y)(x^2+xy+y^2)$ by expanding the right side.


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

*$\implies x^3 - x^2y + x^2y -xy^2 + xy^2 - y^3$

*$\implies x^3 - y^3$


I was wondering what are other ways to prove that $x^3-y^3 = (x-y)(x^2+xy+y^2)$

\begin{align} x^3-y^3 &=x^3\color{red}{-x^2y+x^2y}-y^3\\
&= x^2(x-y)+y(x^2-y^2)\\ 
&= x^2(x-y)+y(x-y)(x+y)\\
 &=(x-y)\Big( x^2+y(x+y)\Big)\\ 
 &=(x-y)( x^2+xy+y^2)
\end{align}
