Algebra Examples

$2 a c - 4 b d + b c - 8 a d$

Step 1

Regroup terms.

$- 8 a d + 2 a c - 4 b d + b c$

Step 2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.1

Group the first two terms and the last two terms.

$(- 8 a d + 2 a c) - 4 b d + b c$

Step 2.2

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

$2 a (- 4 d + c) + b (- 4 d + c)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $- 4 d + c$ .

$(- 4 d + c) (2 a + b)$

Step 4

Factor $- 1$ out of $- 4 d + c$ .

Tap for more steps...

Step 4.1

Reorder $- 4 d$ and $c$ .

$(c - 4 d) (2 a + b)$

Step 4.2

Factor $- 1$ out of $c$ .

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

Step 4.3

Factor $- 1$ out of $- 4 d$ .

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

Step 4.4

Factor $- 1$ out of $- 1 (- c) - (4 d)$ .

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

Step 4.5

Rewrite $- 1 (- c + 4 d)$ as $- (- c + 4 d)$ .

$- (- c + 4 d) (2 a + b)$

Step 5

Factor.

Tap for more steps...

Step 5.1

Factor $- 1$ out of $- c + 4 d$ .

Tap for more steps...

Step 5.1.1

Factor $- 1$ out of $- c$ .

$- (- (c) + 4 d) (2 a + b)$

Step 5.1.2

Factor $- 1$ out of $4 d$ .

$- (- (c) - (- 4 d)) (2 a + b)$

Step 5.1.3

Factor $- 1$ out of $- (c) - (- 4 d)$ .

$- - (c - 4 d) (2 a + b)$

Step 5.2

Remove unnecessary parentheses.

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

Step 6

Combine exponents.

Tap for more steps...

Step 6.1

Factor out negative.

$- ((- (c - 4 d)) (2 a + b))$

Step 6.2

Multiply $- 1$ by $- 1$ .

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

Step 6.3

Multiply $c - 4 d$ by $1$ .

$(c - 4 d) (2 a + b)$