Solve -{3m+(-n+m)-2(m+n)}-2[(+m+n)-(m-n)]

$$- \{ 3 m + ( - n + m ) - 2 ( m + n ) \} - 2 [ ( + m + n ) - ( m - n ) ]$$

Evaluate

$$-2m-n$$

Solution Steps

Combine 3m and m to get 4m.

$$-\left(4m-n-2\left(m+n\right)\right)-2\left(m+n-\left(m-n\right)\right)$$

Use the distributive property to multiply -2 by m+n.

$$-\left(4m-n-2m-2n\right)-2\left(m+n-\left(m-n\right)\right)$$

Combine 4m and -2m to get 2m.

$$-\left(2m-n-2n\right)-2\left(m+n-\left(m-n\right)\right)$$

To find the opposite of 2m-n-2n, find the opposite of each term.

$$-2m-\left(-n\right)-\left(-2n\right)-2\left(m+n-\left(m-n\right)\right)$$

The opposite of -2n is 2n.

$$-2m-\left(-n\right)+2n-2\left(m+n-\left(m-n\right)\right)$$

To find the opposite of m-n, find the opposite of each term.

$$-2m-\left(-n\right)+2n-2\left(m+n-m-\left(-n\right)\right)$$

The opposite of -n is n.

$$-2m-\left(-n\right)+2n-2\left(m+n-m+n\right)$$

Combine m and -m to get 0.

$$-2m-\left(-n\right)+2n-2\left(n+n\right)$$

Combine n and n to get 2n.

$$-2m-\left(-n\right)+2n-2\times 2n$$

Multiply 2 and 2 to get 4.

$$-2m-\left(-n\right)+2n-4n$$

Combine 2n and -4n to get -2n.

$$-2m-\left(-n\right)-2n$$

Multiply -1 and -1 to get 1.

$$-2m+n-2n$$

Combine n and -2n to get -n.

$$-2m-n$$

Expand

$$-2m-n$$

Solution Steps

Combine 3m and m to get 4m.

$$-\left(4m-n-2\left(m+n\right)\right)-2\left(m+n-\left(m-n\right)\right)$$

Use the distributive property to multiply -2 by m+n.

$$-\left(4m-n-2m-2n\right)-2\left(m+n-\left(m-n\right)\right)$$

Combine 4m and -2m to get 2m.

$$-\left(2m-n-2n\right)-2\left(m+n-\left(m-n\right)\right)$$

To find the opposite of 2m-n-2n, find the opposite of each term.

$$-2m-\left(-n\right)-\left(-2n\right)-2\left(m+n-\left(m-n\right)\right)$$

The opposite of -2n is 2n.

$$-2m-\left(-n\right)+2n-2\left(m+n-\left(m-n\right)\right)$$

To find the opposite of m-n, find the opposite of each term.

$$-2m-\left(-n\right)+2n-2\left(m+n-m-\left(-n\right)\right)$$

The opposite of -n is n.

$$-2m-\left(-n\right)+2n-2\left(m+n-m+n\right)$$

Combine m and -m to get 0.

$$-2m-\left(-n\right)+2n-2\left(n+n\right)$$

Combine n and n to get 2n.

$$-2m-\left(-n\right)+2n-2\times 2n$$

Multiply 2 and 2 to get 4.

$$-2m-\left(-n\right)+2n-4n$$

Combine 2n and -4n to get -2n.

$$-2m-\left(-n\right)-2n$$

Multiply -1 and -1 to get 1.

$$-2m+n-2n$$

Combine n and -2n to get -n.

$$-2m-n$$