Pre-Algebra Examples

$\frac{x^{2} y - x y^{2} + x^{2} y^{3}}{\frac{1}{2} \cdot (x y)}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $x y$ out of $x^{2} y - x y^{2} + x^{2} y^{3}$ .

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Step 1.1.1

Factor $x y$ out of $x^{2} y$ .

$\frac{x y (x) - x y^{2} + x^{2} y^{3}}{\frac{1}{2} \cdot x y}$

Step 1.1.2

Factor $x y$ out of $- x y^{2}$ .

$\frac{x y (x) + x y (- 1 y) + x^{2} y^{3}}{\frac{1}{2} \cdot x y}$

Step 1.1.3

Factor $x y$ out of $x^{2} y^{3}$ .

$\frac{x y (x) + x y (- 1 y) + x y (x y^{2})}{\frac{1}{2} \cdot x y}$

Step 1.1.4

Factor $x y$ out of $x y (x) + x y (- 1 y)$ .

$\frac{x y (x - 1 y) + x y (x y^{2})}{\frac{1}{2} \cdot x y}$

Step 1.1.5

Factor $x y$ out of $x y (x - 1 y) + x y (x y^{2})$ .

$\frac{x y (x - 1 y + x y^{2})}{\frac{1}{2} \cdot x y}$

Step 1.2

Rewrite $- 1 y$ as $- y$ .

$\frac{x y (x - y + x y^{2})}{\frac{1}{2} \cdot x y}$

Step 2

Simplify the denominator.

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Step 2.1

Combine $\frac{1}{2}$ and $x$ .

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

Step 2.2

Combine $\frac{x}{2}$ and $y$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Cancel the common factor of $x y$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Apply the distributive property.

$x \cdot 2 - y \cdot 2 + x y^{2} \cdot 2$

Step 6

Simplify.

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Step 6.1

Move $2$ to the left of $x$ .

$2 \cdot x - y \cdot 2 + x y^{2} \cdot 2$

Step 6.2

Multiply $2$ by $- 1$ .

$2 \cdot x - 2 y + x y^{2} \cdot 2$

Step 6.3

Move $2$ to the left of $x y^{2}$ .

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

Step 7

Remove parentheses.

$2 x - 2 y + 2 x y^{2}$