Factor an-mn-n^2+ma

$a n - m n - n^{2} + m a$

Step 1

Reorder terms.

$- n^{2} + a n - m n + a m$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- n^{2} + a n) - m n + a m$

Factor out the greatest common factor (GCF) from each group.

$n (- n + a) + m (- 1 n + a)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $- n + a$ .

$(- n + a) (n + m)$

Step 4

Factor $- 1$ out of $- n + a$ .

Reorder $- n$ and $a$ .

$(a - n) (n + m)$

Factor $- 1$ out of $a$ .

$(- 1 (- a) - n) (n + m)$

Factor $- 1$ out of $- n$ .

$(- 1 (- a) - (n)) (n + m)$

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

$- 1 (- a + n) (n + m)$

Rewrite $- 1 (- a + n)$ as $- (- a + n)$ .

$- (- a + n) (n + m)$

Step 5

Factor.

Factor $- 1$ out of $- a + n$ .

Factor $- 1$ out of $- a$ .

$- (- (a) + n) (n + m)$

Factor $- 1$ out of $n$ .

$- (- (a) - 1 (- n)) (n + m)$

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

$- - (a - n) (n + m)$

Remove unnecessary parentheses.

$- - 1 (a - n) (n + m)$

Step 6

Combine exponents.

Factor out negative.

$- ((- (a - n)) (n + m))$

Multiply $- 1$ by $- 1$ .

$1 ((a - n) (n + m))$

Multiply $a - n$ by $1$ .

$(a - n) (n + m)$