Solve 8(x-2y)^(3)-27(x^2y)^(3)

Evaluate

8 (x - 2 y)^{3} - 27 (x^{2} y)^{3}

Multiply the terms

8 (x - 2 y)^{3} - 27 x^{6} y^{3}

Calculate

- 27 x^{6} y^{3} + 18 x^{4} y^{2} (x - 2 y) - 18 (x - 2 y) \times x^{4} y^{2} + 12 (x - 2 y)^{2} \times x^{2} y - 12 (x - 2 y)^{2} \times x^{2} y + 8 (x - 2 y)^{3}

Rewrite the expression

- 9 x^{4} y^{2} \times 3 x^{2} y + 9 x^{4} y^{2} \times 2 (x - 2 y) - 6 (x - 2 y) \times x^{2} y \times 3 x^{2} y + 6 (x - 2 y) \times x^{2} y \times 2 (x - 2 y) - 4 (x - 2 y)^{2} \times 3 x^{2} y + 4 (x - 2 y)^{2} \times 2 (x - 2 y)

Factor out - 9 x^{4} y^{2} from the expression

- 9 x^{4} y^{2} (3 x^{2} y - 2 (x - 2 y)) - 6 (x - 2 y) \times x^{2} y \times 3 x^{2} y + 6 (x - 2 y) \times x^{2} y \times 2 (x - 2 y) - 4 (x - 2 y)^{2} \times 3 x^{2} y + 4 (x - 2 y)^{2} \times 2 (x - 2 y)

Factor out - 6 (x - 2 y) \times x^{2} y from the expression

- 9 x^{4} y^{2} (3 x^{2} y - 2 (x - 2 y)) - 6 (x - 2 y) \times x^{2} y (3 x^{2} y - 2 (x - 2 y)) - 4 (x - 2 y)^{2} \times 3 x^{2} y + 4 (x - 2 y)^{2} \times 2 (x - 2 y)

Factor out - 4 (x - 2 y)^{2} from the expression

- 9 x^{4} y^{2} (3 x^{2} y - 2 (x - 2 y)) - 6 (x - 2 y) \times x^{2} y (3 x^{2} y - 2 (x - 2 y)) - 4 (x - 2 y)^{2} \times (3 x^{2} y - 2 (x - 2 y))

Factor out 3 x^{2} y - 2 (x - 2 y) from the expression

(- 9 x^{4} y^{2} - 6 (x - 2 y) \times x^{2} y - 4 (x - 2 y)^{2}) (3 x^{2} y - 2 (x - 2 y))

Solution

(- 9 x^{4} y^{2} - 6 x^{3} y + 12 x^{2} y^{2} - 4 x^{2} + 16 x y - 16 y^{2}) (3 x^{2} y - 2 x + 4 y)

Simplify the expression