Factoring

$$x^2-y^2 = (x+y)(x-y)$$
$$x^3+y^3 = (x+y)(x^2-xy+y^2)$$
$$x^3-y^3 = (x-y)(x^2+xy+y^2)$$
$$(x+y)^2 = x^2+2xy+y^2$$
$$(x-y)^2 = x^2-2xy+y^2$$
$$(x+y)^3 = x^3+3x^2{y}+3x{y^2}+y^3$$
$$(x-y)^3 = x^3-3x^2{y}+3x{y^2}-y^3$$
$$x^{2n}-y^{2n} = (x^n-y^n)(x^n+y^n)$$