Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

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 $b = y$ .

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x + y$ .

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Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Divide $2 (x - y)$ by $1$ .

$2 (x - y)$

Step 2.2

Apply the distributive property.

$2 x + 2 (- y)$

Step 2.3

Multiply $- 1$ by $2$ .

$2 x - 2 y$