Factor 4ab+1-2a-2b

$4 a b + 1 - 2 a - 2 b$

Step 1

Regroup terms.

$- 2 a + 4 a b + 1 - 2 b$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- 2 a + 4 a b) + 1 - 2 b$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $- 1 + 2 b$ .

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

Step 4

Factor $- 1$ out of $- 1 + 2 b$ .

Reorder $- 1$ and $2 b$ .

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

Factor $- 1$ out of $2 b$ .

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

Rewrite $- 1$ as $- 1 (1)$ .

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

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

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

Step 5

Factor.

Factor $- 1$ out of $- 2 b + 1$ .

Factor $- 1$ out of $- 2 b$ .

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

Rewrite $1$ as $- 1 (- 1)$ .

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

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

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

Remove unnecessary parentheses.

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

Step 6

Combine exponents.

Factor out negative.

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

Multiply $- 1$ by $- 1$ .

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

Multiply $2 b - 1$ by $1$ .

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