Algebra Examples

$\frac{x^{2} - x y}{y} \times \frac{y^{2}}{x}$

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

Factor $x$ out of $- x y$ .

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

Step 1.1.3

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

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

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

Step 1.2

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

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

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

Step 2

Simplify terms.

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Step 2.1

Combine.

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

Step 2.2

Cancel the common factor of $x$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

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

Step 2.3

Cancel the common factor of $y^{2}$ and $y$ .

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Step 2.3.1

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

$\frac{y ((x - y) y)}{y}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Raise $y$ to the power of $1$ .

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

Step 2.3.2.2

Factor $y$ out of $y^{1}$ .

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

Step 2.3.2.3

Cancel the common factor.

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

Step 2.3.2.4

Rewrite the expression.

$\frac{(x - y) y}{1}$

Step 2.3.2.5

Divide $(x - y) y$ by $1$ .

$(x - y) y$

$(x - y) y$

$(x - y) y$

Step 2.4

Apply the distributive property.

$x y - y \cdot y$

$x y - y \cdot y$

Step 3

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1

Move $y$ .

$x y - (y \cdot y)$

Step 3.2

Multiply $y$ by $y$ .

$x y - y^{2}$

$x y - y^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$