Simplify cube root of 27(x-y)^3

$\sqrt[3]{27 {(x - y)}^{3}}$

Rewrite $27 {(x - y)}^{3}$ as ${(3 (x - y))}^{3}$ .

$\sqrt[3]{{(3 (x - y))}^{3}}$

Pull terms out from under the radical, assuming real numbers.

$3 (x - y)$

Apply the distributive property.

$3 x + 3 (- y)$

Multiply $- 1$ by $3$ .

$3 x - 3 y$