Simplify x square root of 49y^3-y square root of 4x^2y

$x \sqrt{49 y^{3}} - y \sqrt{4 x^{2} y}$

Simplify each term.

Rewrite $49 y^{3}$ as ${(7 y)}^{2} y$ .

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

$x \sqrt{7^{2} y^{3}} - y \sqrt{4 x^{2} y}$

Factor out $y^{2}$ .

$x \sqrt{7^{2} (y^{2} y)} - y \sqrt{4 x^{2} y}$

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

$x \sqrt{{(7 y)}^{2} y} - y \sqrt{4 x^{2} y}$

Pull terms out from under the radical.

$x (7 y \sqrt{y}) - y \sqrt{4 x^{2} y}$

Rewrite using the commutative property of multiplication.

$7 x y \sqrt{y} - y \sqrt{4 x^{2} y}$

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

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

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

Move $y$ .

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

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

$5 x y \sqrt{y}$