Simplify y square root of x^3y-7 square root of x^3y^3+2x square root of xy^3

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

Step 1

Simplify each term.

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

Factor out $x^{2}$ .

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

Add parentheses.

$y \sqrt{x^{2} (x y)} - 7 \sqrt{x^{3} y^{3}} + 2 x \sqrt{x y^{3}}$

Pull terms out from under the radical.

$y (x \sqrt{x y}) - 7 \sqrt{x^{3} y^{3}} + 2 x \sqrt{x y^{3}}$

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

Factor out $x^{2}$ .

$y (x \sqrt{x y}) - 7 \sqrt{x^{2} x y^{3}} + 2 x \sqrt{x y^{3}}$

Factor out $y^{2}$ .

$y (x \sqrt{x y}) - 7 \sqrt{x^{2} x (y^{2} y)} + 2 x \sqrt{x y^{3}}$

Move $x$ .

$y (x \sqrt{x y}) - 7 \sqrt{x^{2} y^{2} x y} + 2 x \sqrt{x y^{3}}$

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

$y (x \sqrt{x y}) - 7 \sqrt{{(x y)}^{2} x y} + 2 x \sqrt{x y^{3}}$

Add parentheses.

$y (x \sqrt{x y}) - 7 \sqrt{{(x y)}^{2} (x y)} + 2 x \sqrt{x y^{3}}$

Pull terms out from under the radical.

$y (x \sqrt{x y}) - 7 (x y \sqrt{x y}) + 2 x \sqrt{x y^{3}}$

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

Factor out $y^{2}$ .

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

Reorder $x$ and $y^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Step 2

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

Reorder $y$ and $x$ .

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

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

$- 6 x y \sqrt{x y} + 2 x (y \sqrt{x y})$

Step 3

Add $- 6 x y \sqrt{x y}$ and $2 x y \sqrt{x y}$ .

$- 4 x y \sqrt{x y}$