Algebra Examples

$2 y \sqrt{x^{3} y} - 5 \sqrt{x^{3} y^{3}} + 8 x \sqrt{x y^{3}}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor out $x^{2}$ .

$2 y \sqrt{x^{2} x y} - 5 \sqrt{x^{3} y^{3}} + 8 x \sqrt{x y^{3}}$

Step 1.1.2

Add parentheses.

$2 y \sqrt{x^{2} (x y)} - 5 \sqrt{x^{3} y^{3}} + 8 x \sqrt{x y^{3}}$

Step 1.2

Pull terms out from under the radical.

$2 y (x \sqrt{x y}) - 5 \sqrt{x^{3} y^{3}} + 8 x \sqrt{x y^{3}}$

Step 1.3

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

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Step 1.3.1

Factor out $x^{2}$ .

$2 y (x \sqrt{x y}) - 5 \sqrt{x^{2} x y^{3}} + 8 x \sqrt{x y^{3}}$

Step 1.3.2

Factor out $y^{2}$ .

$2 y (x \sqrt{x y}) - 5 \sqrt{x^{2} x (y^{2} y)} + 8 x \sqrt{x y^{3}}$

Step 1.3.3

Move $x$ .

$2 y (x \sqrt{x y}) - 5 \sqrt{x^{2} y^{2} x y} + 8 x \sqrt{x y^{3}}$

Step 1.3.4

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

$2 y (x \sqrt{x y}) - 5 \sqrt{{(x y)}^{2} x y} + 8 x \sqrt{x y^{3}}$

Step 1.3.5

Add parentheses.

$2 y (x \sqrt{x y}) - 5 \sqrt{{(x y)}^{2} (x y)} + 8 x \sqrt{x y^{3}}$

Step 1.4

Pull terms out from under the radical.

$2 y (x \sqrt{x y}) - 5 (x y \sqrt{x y}) + 8 x \sqrt{x y^{3}}$

Step 1.5

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

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Step 1.5.1

Factor out $y^{2}$ .

$2 y (x \sqrt{x y}) - 5 x y \sqrt{x y} + 8 x \sqrt{x (y^{2} y)}$

Step 1.5.2

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

$2 y (x \sqrt{x y}) - 5 x y \sqrt{x y} + 8 x \sqrt{y^{2} x y}$

Step 1.5.3

Add parentheses.

$2 y (x \sqrt{x y}) - 5 x y \sqrt{x y} + 8 x \sqrt{y^{2} (x y)}$

Step 1.6

Pull terms out from under the radical.

$2 y (x \sqrt{x y}) - 5 x y \sqrt{x y} + 8 x (y \sqrt{x y})$

Step 2

Subtract $5 x y \sqrt{x y}$ from $2 y (x \sqrt{x y})$ .

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Step 2.1

Move $y$ .

$2 x y \sqrt{x y} - 5 x y \sqrt{x y} + 8 x (y \sqrt{x y})$

Step 2.2

Subtract $5 x y \sqrt{x y}$ from $2 x y \sqrt{x y}$ .

$- 3 x y \sqrt{x y} + 8 x (y \sqrt{x y})$

Step 3

Add $- 3 x y \sqrt{x y}$ and $8 x y \sqrt{x y}$ .

$5 x y \sqrt{x y}$