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

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

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

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