Algebra Examples

$2 a + a c^{2} - a^{2} c - 2 c$

Step 1

Regroup terms.

$- a^{2} c + 2 a + a c^{2} - 2 c$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(- a^{2} c + 2 a) + a c^{2} - 2 c$

Step 2.2

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $- a c + 2$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Rewrite $2$ as $- 1 (- 2)$ .

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

Step 4.3

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

$- (a c - 2) (a - c)$