Solve a^3 (b-a)^3 - b^3

Evaluate

a^{3} (b - a)^{3} - b^{3}

Calculate

a^{3} (b - a)^{3} - a^{2} (b - a)^{2} \times b + a^{2} (b - a)^{2} \times b - a (b - a) \times b^{2} + b^{2} a (b - a) - b^{3}

Rewrite the expression

a^{2} (b - a)^{2} \times a (b - a) - a^{2} (b - a)^{2} \times b + a (b - a) \times ba (b - a) - a (b - a) \times b \times b + b^{2} a (b - a) - b^{2} \times b

Factor out a^{2} (b - a)^{2} from the expression

a^{2} (b - a)^{2} \times (a (b - a) - b) + a (b - a) \times ba (b - a) - a (b - a) \times b \times b + b^{2} a (b - a) - b^{2} \times b

Factor out a (b - a) \times b from the expression

a^{2} (b - a)^{2} \times (a (b - a) - b) + a (b - a) \times b (a (b - a) - b) + b^{2} a (b - a) - b^{2} \times b

Factor out b^{2} from the expression

a^{2} (b - a)^{2} \times (a (b - a) - b) + a (b - a) \times b (a (b - a) - b) + b^{2} (a (b - a) - b)

Factor out a (b - a) - b from the expression

(a^{2} (b - a)^{2} + a (b - a) \times b + b^{2}) (a (b - a) - b)

Solution

(a^{2} b^{2} - 2 a^{3} b + a^{4} + a b^{2} - a^{2} b + b^{2}) (ab - a^{2} - b)

Simplify the expression