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

Evaluate

(ab)^{3} - (b - c)^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(ab - (b - c)) ((ab)^{2} + ab (b - c) + (b - c)^{2})

To raise a product to a power,raise each factor to that power

(ab - (b - c)) (a^{2} b^{2} + ab (b - c) + (b - c)^{2})

Factor the expression

(ab - b + c) (a^{2} b^{2} + ab (b - c) + (b - c)^{2})

Solution

More Steps

(ab - b + c) (a^{2} b^{2} + a b^{2} - ab c + b^{2} - 2 b c + c^{2})

Simplify the expression