Basic Math Examples

$- 6 m p + 4 m + 18 p - 12$

Step 1

Factor $2$ out of $- 6 m p + 4 m + 18 p - 12$ .

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Step 1.1

Factor $2$ out of $- 6 m p$ .

$2 (- 3 m p) + 4 m + 18 p - 12$

Step 1.2

Factor $2$ out of $4 m$ .

$2 (- 3 m p) + 2 (2 m) + 18 p - 12$

Step 1.3

Factor $2$ out of $18 p$ .

$2 (- 3 m p) + 2 (2 m) + 2 (9 p) - 12$

Step 1.4

Factor $2$ out of $- 12$ .

$2 (- 3 m p) + 2 (2 m) + 2 (9 p) + 2 (- 6)$

Step 1.5

Factor $2$ out of $2 (- 3 m p) + 2 (2 m)$ .

$2 (- 3 m p + 2 m) + 2 (9 p) + 2 (- 6)$

Step 1.6

Factor $2$ out of $2 (- 3 m p + 2 m) + 2 (9 p)$ .

$2 (- 3 m p + 2 m + 9 p) + 2 (- 6)$

Step 1.7

Factor $2$ out of $2 (- 3 m p + 2 m + 9 p) + 2 (- 6)$ .

$2 (- 3 m p + 2 m + 9 p - 6)$

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.

$2 ((- 3 m p + 2 m) + 9 p - 6)$

Step 2.2

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

$2 (m (- 3 p + 2) - 3 (- 3 p + 2))$

Step 3

Factor.

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Step 3.1

Factor the polynomial by factoring out the greatest common factor, $- 3 p + 2$ .

$2 ((- 3 p + 2) (m - 3))$

Step 3.2

Remove unnecessary parentheses.

$2 (- 3 p + 2) (m - 3)$

Step 4

Factor.

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Step 4.1

Factor $- 1$ out of $- 3 p + 2$ .

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Step 4.1.1

Factor $- 1$ out of $- 3 p$ .

$2 (- (3 p) + 2) (m - 3)$

Step 4.1.2

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

$2 (- (3 p) - 1 (- 2)) (m - 3)$

Step 4.1.3

Factor $- 1$ out of $- (3 p) - 1 (- 2)$ .

$2 (- (3 p - 2)) (m - 3)$

Step 4.2

Remove unnecessary parentheses.

$2 \cdot - 1 (3 p - 2) (m - 3)$

Step 5

Factor.

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Step 5.1

Combine exponents.

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Step 5.1.1

Factor out negative.

$- ((2 (3 p - 2)) (m - 3))$

Step 5.1.2

Multiply $2$ by $- 1$ .

$- 2 ((3 p - 2) (m - 3))$

Step 5.2

Remove unnecessary parentheses.

$- 2 (3 p - 2) (m - 3)$