Basic Math Examples

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

Step 1

Simplify by adding terms.

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Step 1.1

Remove parentheses.

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

Step 1.2

Combine the opposite terms in $(m + n) - 2 (a - m) (m + n) + a - m$ .

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Step 1.2.1

Subtract $m$ from $m$ .

$(n) - 2 (a - m) (m + n) + a + 0$

Step 1.2.2

Add $(n) - 2 (a - m) (m + n) + a$ and $0$ .

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $- 1$ by $- 2$ .

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

Step 2.3

Expand $(- 2 a + 2 m) (m + n)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

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

Step 2.3.2

Apply the distributive property.

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

Step 2.3.3

Apply the distributive property.

$n - 2 a m - 2 a n + 2 m \cdot m + 2 m n + a$

Step 2.4

Multiply $m$ by $m$ by adding the exponents.

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Step 2.4.1

Move $m$ .

$n - 2 a m - 2 a n + 2 (m \cdot m) + 2 m n + a$

Step 2.4.2

Multiply $m$ by $m$ .

$n - 2 a m - 2 a n + 2 m^{2} + 2 m n + a$

Step 3

Simplify the expression.

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Step 3.1

Move $n$ .

$- 2 a m - 2 a n + 2 m^{2} + 2 m n + a + n$

Step 3.2

Move $2 m^{2}$ .

$- 2 a m - 2 a n + 2 m n + 2 m^{2} + a + n$

Step 3.3

Reorder $- 2 a m$ and $- 2 a n$ .

$- 2 a n - 2 a m + 2 m n + 2 m^{2} + a + n$