Let (a+b) is a binomial
Its cube = (a+b)^3
= (a+b) (a+b)^2
= (a+b)[a^2 + 2ab + b^2] { expansion of (a+b)^2 }
= a(a^2 + 2ab + b^2) + b (a^2 + 2ab + b^2) [ distributive property]
= a^3 + 2a^2*b + a*b^2+ a^2 *b + 2a *b^2 + b^3
(a+b)^3 = a^3 +3a^2*b + 3a*b^2 + b^3