Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Factor out $y^{2}$ .

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

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

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Step 1.3.1

Factor out $y^{2}$ .

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

Step 1.3.2

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

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

$0$