Solve (3)(-m+n)*(-m-n)

$$( 3 ) ( - m + n ) \cdot ( - m - n )$$

Evaluate

$$3\left(m^{2}-n^{2}\right)$$

Solution Steps

Use the distributive property to multiply 3 by -m+n.

$$\left(3\left(-m\right)+3n\right)\left(-m-n\right)$$

Apply the distributive property by multiplying each term of 3\left(-m\right)+3n by each term of -m-n.

$$3\left(-m\right)^{2}-3\left(-m\right)n+3n\left(-m\right)-3n^{2}$$

Calculate -m to the power of 2 and get m^{2}.

$$3m^{2}-3\left(-m\right)n+3n\left(-m\right)-3n^{2}$$

Multiply -3 and -1 to get 3.

$$3m^{2}+3mn+3n\left(-m\right)-3n^{2}$$

Multiply 3 and -1 to get -3.

$$3m^{2}+3mn-3nm-3n^{2}$$

Combine 3mn and -3nm to get 0.

$$3m^{2}-3n^{2}$$

Expand

$$3m^{2}-3n^{2}$$

Solution Steps

Use the distributive property to multiply 3 by -m+n.

$$\left(3\left(-m\right)+3n\right)\left(-m-n\right)$$

Apply the distributive property by multiplying each term of 3\left(-m\right)+3n by each term of -m-n.

$$3\left(-m\right)^{2}-3\left(-m\right)n+3n\left(-m\right)-3n^{2}$$

Calculate -m to the power of 2 and get m^{2}.

$$3m^{2}-3\left(-m\right)n+3n\left(-m\right)-3n^{2}$$

Multiply -3 and -1 to get 3.

$$3m^{2}+3mn+3n\left(-m\right)-3n^{2}$$

Multiply 3 and -1 to get -3.

$$3m^{2}+3mn-3nm-3n^{2}$$

Combine 3mn and -3nm to get 0.

$$3m^{2}-3n^{2}$$