Algebra Examples

$- m - n + x (m + n)$

Step 1

Factor $- 1$ out of $- m - n + x (m + n)$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $- n$ .

$- m + x (m + n) - n$

Step 1.1.2

Reorder $- m$ and $x (m + n)$ .

$x (m + n) - m - n$

Step 1.2

Factor $- 1$ out of $x (m + n)$ .

$- (- x (m + n)) - m - n$

Step 1.3

Factor $- 1$ out of $- m$ .

$- (- x (m + n)) - (m) - n$

Step 1.4

Factor $- 1$ out of $- n$ .

$- (- x (m + n)) - (m) - (n)$

Step 1.5

Factor $- 1$ out of $- (- x (m + n)) - (m)$ .

$- (- x (m + n) + m) - (n)$

Step 1.6

Factor $- 1$ out of $- (- x (m + n) + m) - (n)$ .

$- (- x (m + n) + m + n)$

Step 2

Apply the distributive property.

$- (- x m - x n + m + n)$

Step 3

Factor.

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Step 3.1

Rewrite $- x m - x n + m + n$ in a factored form.

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Step 3.1.1

Factor out the greatest common factor from each group.

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Step 3.1.1.1

Group the first two terms and the last two terms.

$- ((- x m - x n) + m + n)$

Step 3.1.1.2

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

$- (x (- 1 m - 1 n) - 1 (- m - n))$

Step 3.1.2

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

$- ((- 1 m - 1 n) (x - 1))$

Step 3.1.3

Rewrite $- 1 m$ as $- m$ .

$- ((- m - 1 n) (x - 1))$

Step 3.1.4

Rewrite $- 1 n$ as $- n$ .

$- ((- m - n) (x - 1))$

Step 3.2

Remove unnecessary parentheses.

$- (- m - n) (x - 1)$

Step 4

Factor.

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Step 4.1

Factor $- 1$ out of $- m - n$ .

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Step 4.1.1

Factor $- 1$ out of $- m$ .

$- (- (m) - n) (x - 1)$

Step 4.1.2

Factor $- 1$ out of $- n$ .

$- (- (m) - (n)) (x - 1)$

Step 4.1.3

Factor $- 1$ out of $- (m) - (n)$ .

$- - (m + n) (x - 1)$

Step 4.2

Remove unnecessary parentheses.

$- - 1 (m + n) (x - 1)$

Step 5

Combine exponents.

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Step 5.1

Factor out negative.

$- ((- (m + n)) (x - 1))$

Step 5.2

Multiply $- 1$ by $- 1$ .

$1 ((m + n) (x - 1))$

Step 5.3

Multiply $m + n$ by $1$ .

$(m + n) (x - 1)$