Factor xk-xy-x^2+yk

$x k - x y - x^{2} + y k$

Step 1

Reorder terms.

$- x^{2} + k x - x y + k y$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- x^{2} + k x) - x y + k y$

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

$x (- x + k) + y (- x + k)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $- x + k$ .

$(- x + k) (x + y)$

Step 4

Factor $- 1$ out of $- x + k$ .

Reorder $- x$ and $k$ .

$(k - x) (x + y)$

Factor $- 1$ out of $k$ .

$(- 1 (- k) - x) (x + y)$

Factor $- 1$ out of $- x$ .

$(- 1 (- k) - (x)) (x + y)$

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

$- 1 (- k + x) (x + y)$

Rewrite $- 1 (- k + x)$ as $- (- k + x)$ .

$- (- k + x) (x + y)$

Step 5

Factor.

Factor $- 1$ out of $- k + x$ .

Factor $- 1$ out of $- k$ .

$- (- (k) + x) (x + y)$

Factor $- 1$ out of $x$ .

$- (- (k) - 1 (- x)) (x + y)$

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

$- - (k - x) (x + y)$

Remove unnecessary parentheses.

$- - 1 (k - x) (x + y)$

Step 6

Combine exponents.

Factor out negative.

$- ((- (k - x)) (x + y))$

Multiply $- 1$ by $- 1$ .

$1 ((k - x) (x + y))$

Multiply $k - x$ by $1$ .

$(k - x) (x + y)$