Simplify 2 square root of 32x^2y^3-xy square root of 98y

$2 \sqrt{32 x^{2} y^{3}} - x y \sqrt{98 y}$

Step 1

Simplify each term.

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

Factor $16$ out of $32$ .

$2 \sqrt{16 (2) x^{2} y^{3}} - x y \sqrt{98 y}$

Rewrite $16$ as $4^{2}$ .

$2 \sqrt{4^{2} \cdot 2 x^{2} y^{3}} - x y \sqrt{98 y}$

Factor out $y^{2}$ .

$2 \sqrt{4^{2} \cdot 2 x^{2} (y^{2} y)} - x y \sqrt{98 y}$

Move $2$ .

$2 \sqrt{4^{2} x^{2} y^{2} \cdot 2 y} - x y \sqrt{98 y}$

Rewrite $4^{2} x^{2} y^{2}$ as ${(4 x y)}^{2}$ .

$2 \sqrt{{(4 x y)}^{2} \cdot 2 y} - x y \sqrt{98 y}$

Add parentheses.

$2 \sqrt{{(4 x y)}^{2} \cdot (2 y)} - x y \sqrt{98 y}$

Pull terms out from under the radical.

$2 (4 x y \sqrt{2 y}) - x y \sqrt{98 y}$

Multiply $4$ by $2$ .

$8 (x y \sqrt{2 y}) - x y \sqrt{98 y}$

Rewrite $98 y$ as $7^{2} \cdot (2 y)$ .

Factor $49$ out of $98$ .

$8 x y \sqrt{2 y} - x y \sqrt{49 (2) y}$

Rewrite $49$ as $7^{2}$ .

$8 x y \sqrt{2 y} - x y \sqrt{7^{2} \cdot 2 y}$

Add parentheses.

$8 x y \sqrt{2 y} - x y \sqrt{7^{2} \cdot (2 y)}$

Pull terms out from under the radical.

$8 x y \sqrt{2 y} - x y (7 \sqrt{2 y})$

Multiply $7$ by $- 1$ .

$8 x y \sqrt{2 y} - 7 x y \sqrt{2 y}$

Step 2

Simplify by adding terms.

Subtract $7 x y \sqrt{2 y}$ from $8 x y \sqrt{2 y}$ .

$1 x y \sqrt{2 y}$

Multiply $x$ by $1$ .

$x y \sqrt{2 y}$