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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of m+n by each term of a-2.

$$ma-2m+na-2n-\left(m-n\right)\left(a-2\right)$$

Apply the distributive property by multiplying each term of m-n by each term of a-2.

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

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

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

Combine ma and -ma to get 0.

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

The opposite of -2m is 2m.

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

Combine -2m and 2m to get 0.

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

The opposite of -na is na.

$$na-2n+na-2n$$

Combine na and na to get 2na.

$$2na-2n-2n$$

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

$$2na-4n$$

Expand

$$2an-4n$$

Solution Steps

Apply the distributive property by multiplying each term of m+n by each term of a-2.

$$ma-2m+na-2n-\left(m-n\right)\left(a-2\right)$$

Apply the distributive property by multiplying each term of m-n by each term of a-2.

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

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

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

Combine ma and -ma to get 0.

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

The opposite of -2m is 2m.

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

Combine -2m and 2m to get 0.

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

The opposite of -na is na.

$$na-2n+na-2n$$

Combine na and na to get 2na.

$$2na-2n-2n$$

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

$$2na-4n$$