Factor 2ab-2ac+2a-b+c-1

$2 a b - 2 a c + 2 a - b + c - 1$

Step 1

Regroup terms.

$2 a b - b - 2 a c + 2 a + c - 1$

Step 2

Factor $b$ out of $2 a b - b$ .

Factor $b$ out of $2 a b$ .

$b (2 a) - b - 2 a c + 2 a + c - 1$

Factor $b$ out of $- b$ .

$b (2 a) + b \cdot - 1 - 2 a c + 2 a + c - 1$

Factor $b$ out of $b (2 a) + b \cdot - 1$ .

$b (2 a - 1) - 2 a c + 2 a + c - 1$

Step 3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$b (2 a - 1) + (- 2 a c + 2 a) + c - 1$

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

$b (2 a - 1) + 2 a (- 1 c + 1) - 1 (- c + 1)$

Step 4

Factor the polynomial by factoring out the greatest common factor, $- 1 c + 1$ .

$b (2 a - 1) + (- 1 c + 1) (2 a - 1)$

Step 5

Rewrite $- 1 c$ as $- c$ .

$b (2 a - 1) + (- c + 1) (2 a - 1)$

Step 6

Factor $2 a - 1$ out of $b (2 a - 1) + (- c + 1) (2 a - 1)$ .

Factor $2 a - 1$ out of $b (2 a - 1)$ .

$(2 a - 1) b + (- c + 1) (2 a - 1)$

Factor $2 a - 1$ out of $(- c + 1) (2 a - 1)$ .

$(2 a - 1) b + (2 a - 1) (- c + 1)$

Factor $2 a - 1$ out of $(2 a - 1) b + (2 a - 1) (- c + 1)$ .

$(2 a - 1) (b - c + 1)$