Simplify (a-y)/(w+n)*(w^2-n^2)/(y-a)

$\frac{a - y}{w + n} \cdot \frac{w^{2} - n^{2}}{y - a}$

Step 1

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

$\frac{a - y}{w + n} \cdot \frac{(w + n) (w - n)}{y - a}$

Step 2

Simplify terms.

Cancel the common factor of $w + n$ .

Cancel the common factor.

$\frac{a - y}{w + n} \cdot \frac{(w + n) (w - n)}{y - a}$

Rewrite the expression.

$(a - y) \cdot \frac{w - n}{y - a}$

Multiply $a - y$ by $\frac{w - n}{y - a}$ .

$\frac{(a - y) (w - n)}{y - a}$

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

Factor $- 1$ out of $a$ .

$\frac{(- 1 (- a) - y) (w - n)}{y - a}$

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

$\frac{(- 1 (- a) - (y)) (w - n)}{y - a}$

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

$\frac{- 1 (- a + y) (w - n)}{y - a}$

Reorder terms.

$\frac{- 1 (- a + y) (w - n)}{- a + y}$

Cancel the common factor.

$\frac{- 1 (- a + y) (w - n)}{- a + y}$

Divide $- 1 (w - n)$ by $1$ .

$- 1 (w - n)$

Rewrite $- 1 (w - n)$ as $- (w - n)$ .

$- (w - n)$

Apply the distributive property.

$- w - - n$

Step 3

Multiply $- - n$ .

Multiply $- 1$ by $- 1$ .

$- w + 1 n$

Multiply $n$ by $1$ .

$- w + n$