Simplify cube root of 16xy^3-y cube root of 128x

$\sqrt[3]{16 x y^{3}} - y \sqrt[3]{128 x}$

Step 1

Simplify each term.

Rewrite $16 x y^{3}$ as ${(2 y)}^{3} \cdot (2 x)$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2) x y^{3}} - y \sqrt[3]{128 x}$

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} \cdot 2 x y^{3}} - y \sqrt[3]{128 x}$

Move $x$ .

$\sqrt[3]{2^{3} \cdot 2 y^{3} x} - y \sqrt[3]{128 x}$

Move $2$ .

$\sqrt[3]{2^{3} y^{3} \cdot 2 x} - y \sqrt[3]{128 x}$

Rewrite $2^{3} y^{3}$ as ${(2 y)}^{3}$ .

$\sqrt[3]{{(2 y)}^{3} \cdot 2 x} - y \sqrt[3]{128 x}$

Add parentheses.

$\sqrt[3]{{(2 y)}^{3} \cdot (2 x)} - y \sqrt[3]{128 x}$

Pull terms out from under the radical.

$2 y \sqrt[3]{2 x} - y \sqrt[3]{128 x}$

Rewrite $128 x$ as $4^{3} \cdot (2 x)$ .

Factor $64$ out of $128$ .

$2 y \sqrt[3]{2 x} - y \sqrt[3]{64 (2) x}$

Rewrite $64$ as $4^{3}$ .

$2 y \sqrt[3]{2 x} - y \sqrt[3]{4^{3} \cdot 2 x}$

Add parentheses.

$2 y \sqrt[3]{2 x} - y \sqrt[3]{4^{3} \cdot (2 x)}$

Pull terms out from under the radical.

$2 y \sqrt[3]{2 x} - y (4 \sqrt[3]{2 x})$

Multiply $4$ by $- 1$ .

$2 y \sqrt[3]{2 x} - 4 y \sqrt[3]{2 x}$

Step 2

Subtract $4 y \sqrt[3]{2 x}$ from $2 y \sqrt[3]{2 x}$ .

$- 2 y \sqrt[3]{2 x}$