Algebra Examples

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

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

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

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Factor $x$ out of $x y$ .

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

Step 2.1.3

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

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

Step 2.2

Cancel the common factor of $x + y$ .

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.3

Multiply $\frac{x - y}{x - y}$ by $\frac{2 x y}{x}$ .

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

Step 2.4

Cancel the common factor of $x - y$ .

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Step 2.4.1

Cancel the common factor.

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

Step 2.4.2

Rewrite the expression.

$\frac{2 x y}{x}$

Step 2.5

Cancel the common factor of $x$ .

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Step 2.5.1

Cancel the common factor.

$\frac{2 x y}{x}$

Step 2.5.2

Divide $2 y$ by $1$ .

$2 y$