Simplify (x^2-y^2)/6*12/(x-y)

$\frac{x^{2} - y^{2}}{6} \cdot \frac{12}{x - y}$

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 $b = y$ .

$\frac{(x + y) (x - y)}{6} \cdot \frac{12}{x - y}$

Step 2

Simplify terms.

Cancel the common factor of $x - y$ .

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

$\frac{(x - y) (x + y)}{6} \cdot \frac{12}{x - y}$

Cancel the common factor.

$\frac{(x - y) (x + y)}{6} \cdot \frac{12}{x - y}$

Rewrite the expression.

$\frac{x + y}{6} \cdot 12$

Simplify terms.

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$\frac{x + y}{6} \cdot (6 (2))$

Cancel the common factor.

$\frac{x + y}{6} \cdot (6 \cdot 2)$

Rewrite the expression.

$(x + y) \cdot 2$

Apply the distributive property.

$x \cdot 2 + y \cdot 2$

Reorder.

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

$2 \cdot x + y \cdot 2$

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

$2 \cdot x + 2 \cdot y$

Multiply $2$ by $y$ .

$2 x + 2 y$