\(\left(x+y\right)^2=x^2+2xy+y^2\)
\(\left(x-y\right)^2=x^2-2xy+y^2\)
\(\left(x-y\right)\left(x+y\right)=x^2-y^2\)
\(\left(x-y\right)\left(x^2+xy+y^2\right)=x^3-y^3\)
\(\left(x+y\right)\left(x^2-xy+y^2\right)=x^3+y^3\)
\(\left(x+y\right)^3=x^3+3x^2y+3xy^2+y^3\)
\(\left(x-y\right)^3=x^3-3x^2y+3xy^2-y^3\)