Factor 6bx-3by+2cx-cy+4dx-2dy

$6 b x - 3 b y + 2 c x - c y + 4 d x - 2 d y$

Step 1

Regroup terms.

$6 b x - 3 b y + 2 c x - c y + 4 d x - 2 d y$

Step 2

Factor $3 b$ out of $6 b x - 3 b y$ .

Factor $3 b$ out of $6 b x$ .

$3 b (2 x) - 3 b y + 2 c x - c y + 4 d x - 2 d y$

Factor $3 b$ out of $- 3 b y$ .

$3 b (2 x) + 3 b (- 1 y) + 2 c x - c y + 4 d x - 2 d y$

Factor $3 b$ out of $3 b (2 x) + 3 b (- 1 y)$ .

$3 b (2 x - 1 y) + 2 c x - c y + 4 d x - 2 d y$

Step 3

Rewrite $- 1 y$ as $- y$ .

$3 b (2 x - y) + 2 c x - c y + 4 d x - 2 d y$

Step 4

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 b (2 x - y) + (2 c x - c y) + 4 d x - 2 d y$

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

$3 b (2 x - y) + c (2 x - 1 y) + 2 d (2 x - 1 y)$

Step 5

Factor the polynomial by factoring out the greatest common factor, $2 x - 1 y$ .

$3 b (2 x - y) + (2 x - 1 y) (c + 2 d)$

Step 6

Rewrite $- 1 y$ as $- y$ .

$3 b (2 x - y) + (2 x - y) (c + 2 d)$

Step 7

Factor $2 x - y$ out of $3 b (2 x - y) + (2 x - y) (c + 2 d)$ .

Factor $2 x - y$ out of $3 b (2 x - y)$ .

$(2 x - y) (3 b) + (2 x - y) (c + 2 d)$

Factor $2 x - y$ out of $(2 x - y) (3 b) + (2 x - y) (c + 2 d)$ .

$(2 x - y) (3 b + c + 2 d)$