$$(a+b)(a-b)$$ = $$\displaystyle (a^2-b^2)$$
$$(a^3-b^3)$$ = $$\displaystyle (a-b)(a^2+b^2+ab)$$
$$(a^3+b^3)$$ = $$\displaystyle (a+b)(a^2+b^2-ab)$$
$$(a+b+c)^2$$ = $$\displaystyle a^2+b^2+c^2+2(ab+bc+ca)$$
$$\displaystyle (a^3+b^3+c^3-3abc)$$ = $$\displaystyle (a+b+c) * (a^2+b^2+c^2 - ab - bc - ca)$$
If $$(a+b+c)=0$$ => $$\displaystyle a^3+b^3+c^3=3abc$$
$$(a+b)^2$$ = $$\displaystyle (a^2+b^2+2ab)$$
$$(a-b)^2$$ = $$\displaystyle (a^2+b^2-2ab)$$
$$(a+b)^3$$ = $$\displaystyle a^3+b^3+3ab(a+b)$$
$$(a-b)^3$$ = $$\displaystyle a^3-b^3-3ab(a-b)$$
