Simplify the Radical Expression 5 cube root of 32x^3y^4-3xy cube root of 4y

$5 \sqrt[3]{32 x^{3} y^{4}} - 3 x y \sqrt[3]{4 y}$

Step 1

Simplify each term.

Rewrite $32 x^{3} y^{4}$ as ${(2 x y)}^{3} \cdot (4 y)$ .

Factor $8$ out of $32$ .

$5 \sqrt[3]{8 (4) x^{3} y^{4}} - 3 x y \sqrt[3]{4 y}$

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

$5 \sqrt[3]{2^{3} \cdot 4 x^{3} y^{4}} - 3 x y \sqrt[3]{4 y}$

Factor out $y^{3}$ .

$5 \sqrt[3]{2^{3} \cdot 4 x^{3} (y^{3} y)} - 3 x y \sqrt[3]{4 y}$

Move $4$ .

$5 \sqrt[3]{2^{3} x^{3} y^{3} \cdot 4 y} - 3 x y \sqrt[3]{4 y}$

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

$5 \sqrt[3]{{(2 x y)}^{3} \cdot 4 y} - 3 x y \sqrt[3]{4 y}$

Add parentheses.

$5 \sqrt[3]{{(2 x y)}^{3} \cdot (4 y)} - 3 x y \sqrt[3]{4 y}$

Pull terms out from under the radical.

$5 (2 x y \sqrt[3]{4 y}) - 3 x y \sqrt[3]{4 y}$

Multiply $2$ by $5$ .

$10 x y \sqrt[3]{4 y} - 3 x y \sqrt[3]{4 y}$

Step 2

Subtract $3 x y \sqrt[3]{4 y}$ from $10 x y \sqrt[3]{4 y}$ .

$7 x y \sqrt[3]{4 y}$