Algebra Examples

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

Step 1

Regroup terms.

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

Step 2

Factor $- b$ out of $- b c + b$ .

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Step 2.1

Factor $- b$ out of $- b c$ .

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

Step 2.2

Rewrite $b$ as $1 b$ .

$- b (c) + 1 b + a c - a + c^{2} - c$

Step 2.3

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

$- b (c) - b (- 1) + a c - a + c^{2} - c$

Step 2.4

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

$- b (c - 1) + a c - a + c^{2} - c$

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

$- b (c - 1) + (a c - a) + c^{2} - c$

Step 3.2

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

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

Step 6

Factor.

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Step 6.1

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

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Step 6.1.1

Reorder $- b$ and $a$ .

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

Step 6.1.2

Factor $- 1$ out of $a$ .

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

Step 6.1.3

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

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

Step 6.1.4

Factor $- 1$ out of $c$ .

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

Step 6.1.5

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

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

Step 6.1.6

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

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

Step 6.1.7

Rewrite $- 1 (- a + b - c)$ as $- (- a + b - c)$ .

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

Step 6.2

Remove unnecessary parentheses.

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

Step 7

Factor out negative.

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

Step 8

Remove unnecessary parentheses.

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

Step 9

Factor.

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Step 9.1

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

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Step 9.1.1

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

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

Step 9.1.2

Factor $- 1$ out of $b$ .

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

Step 9.1.3

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

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

Step 9.1.4

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

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

Step 9.1.5

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

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

Step 9.2

Remove unnecessary parentheses.

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

Step 10

Combine exponents.

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Step 10.1

Factor out negative.

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

Step 10.2

Multiply $- 1$ by $- 1$ .

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

Step 10.3

Multiply $c - 1$ by $1$ .

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