Basic Math Examples

$m (a - 2 b) + n (2 b - a)$

Step 1

Apply the distributive property.

$m a + m (- 2 b) + n (2 b - a)$

Step 2

Rewrite using the commutative property of multiplication.

$m a - 2 m b + n (2 b - a)$

Step 3

Apply the distributive property.

$m a - 2 m b + n (2 b) + n (- a)$

Step 4

Rewrite using the commutative property of multiplication.

$m a - 2 m b + 2 n b + n (- a)$

Step 5

Rewrite using the commutative property of multiplication.

$m a - 2 m b + 2 n b - n a$

Step 6

Rewrite $m a - 2 m b + 2 n b - n a$ in a factored form.

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Step 6.1

Regroup terms.

$- 2 m b + m a + 2 n b - n a$

Step 6.2

Factor out the greatest common factor from each group.

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Step 6.2.1

Group the first two terms and the last two terms.

$(- 2 m b + m a) + 2 n b - n a$

Step 6.2.2

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

$m (- 2 b + a) - n (- 2 b + a)$

Step 6.3

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

$(- 2 b + a) (m - n)$

Step 7

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

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Step 7.1

Reorder $- 2 b$ and $a$ .

$(a - 2 b) (m - n)$

Step 7.2

Factor $- 1$ out of $a$ .

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

Step 7.3

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

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

Step 7.4

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

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

Step 7.5

Rewrite $- 1 (- a + 2 b)$ as $- (- a + 2 b)$ .

$- (- a + 2 b) (m - n)$

Step 8

Factor.

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Step 8.1

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

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Step 8.1.1

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

$- (- (a) + 2 b) (m - n)$

Step 8.1.2

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

$- (- (a) - (- 2 b)) (m - n)$

Step 8.1.3

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

$- - (a - 2 b) (m - n)$

Step 8.2

Remove unnecessary parentheses.

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

Step 9

Combine exponents.

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Step 9.1

Factor out negative.

$- ((- (a - 2 b)) (m - n))$

Step 9.2

Multiply $- 1$ by $- 1$ .

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

Step 9.3

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

$(a - 2 b) (m - n)$