Factor ax+ay+bx+by-cx-cy

$a x + a y + b x + b y - c x - c y$

Regroup terms.

$a x + b x - c x + a y + b y - c y$

Factor $x$ out of $a x + b x - c x$ .

Factor $x$ out of $a x$ .

$x a + b x - c x + a y + b y - c y$

Factor $x$ out of $b x$ .

$x a + x b - c x + a y + b y - c y$

Factor $x$ out of $- c x$ .

$x a + x b + x (- c) + a y + b y - c y$

Factor $x$ out of $x a + x b$ .

$x (a + b) + x (- c) + a y + b y - c y$

Factor $x$ out of $x (a + b) + x (- c)$ .

$x (a + b - c) + a y + b y - c y$

Factor $y$ out of $a y + b y - c y$ .

Factor $y$ out of $a y$ .

$x (a + b - c) + y a + b y - c y$

Factor $y$ out of $b y$ .

$x (a + b - c) + y a + y b - c y$

Factor $y$ out of $- c y$ .

$x (a + b - c) + y a + y b + y (- c)$

Factor $y$ out of $y a + y b$ .

$x (a + b - c) + y (a + b) + y (- c)$

Factor $y$ out of $y (a + b) + y (- c)$ .

$x (a + b - c) + y (a + b - c)$

Factor $a + b - c$ out of $x (a + b - c) + y (a + b - c)$ .

Factor $a + b - c$ out of $x (a + b - c)$ .

$(a + b - c) x + y (a + b - c)$

Factor $a + b - c$ out of $y (a + b - c)$ .

$(a + b - c) x + (a + b - c) y$

Factor $a + b - c$ out of $(a + b - c) x + (a + b - c) y$ .

$(a + b - c) (x + y)$