Algebra Examples

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

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 $b = y$ .

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x - y$ and $y - x$ .

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Step 2.1.1

Factor $- 1$ out of $x$ .

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

Step 2.1.2

Factor $- 1$ out of $- y$ .

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

Step 2.1.3

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

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

Step 2.1.4

Reorder terms.

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

Step 2.1.5

Cancel the common factor.

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

Step 2.1.6

Divide $(x + y) \cdot (- 1)$ by $1$ .

$(x + y) \cdot (- 1)$

Step 2.2

Simplify by multiplying through.

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Step 2.2.1

Apply the distributive property.

$x \cdot - 1 + y \cdot - 1$

Step 2.2.2

Reorder.

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Step 2.2.2.1

Move $- 1$ to the left of $x$ .

$- 1 \cdot x + y \cdot - 1$

Step 2.2.2.2

Move $- 1$ to the left of $y$ .

$- 1 \cdot x - 1 \cdot y$

Step 2.3

Simplify each term.

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Step 2.3.1

Rewrite $- 1 x$ as $- x$ .

$- x - 1 \cdot y$

Step 2.3.2

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

$- x - y$