Solve m(m-3n)-n(m-3n)

$$m ( m - 3 n ) - n ( m - 3 n )$$

Evaluate

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

Solution Steps

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

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

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

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

To find the opposite of nm-3n^{2}, find the opposite of each term.

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

The opposite of -3n^{2} is 3n^{2}.

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

Combine -3mn and -nm to get -4mn.

$$m^{2}-4mn+3n^{2}$$

Expand

$$m^{2}-4mn+3n^{2}$$

Solution Steps

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

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

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

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

To find the opposite of nm-3n^{2}, find the opposite of each term.

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

The opposite of -3n^{2} is 3n^{2}.

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

Combine -3mn and -nm to get -4mn.

$$m^{2}-4mn+3n^{2}$$