Solve [(m-6)+n][(m-6)-n]

$$[ ( m - 6 ) + n ] [ ( m - 6 ) - n ]$$

Evaluate

$$\left(m-6\right)^{2}-n^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of m-6+n by each term of m-6-n.

$$m^{2}-6m-mn-6m+36+6n+nm-6n-n^{2}$$

Combine -6m and -6m to get -12m.

$$m^{2}-12m-mn+36+6n+nm-6n-n^{2}$$

Combine -mn and nm to get 0.

$$m^{2}-12m+36+6n-6n-n^{2}$$

Combine 6n and -6n to get 0.

$$m^{2}-12m+36-n^{2}$$

Expand

$$m^{2}-12m-n^{2}+36$$

Solution Steps

Apply the distributive property by multiplying each term of m-6+n by each term of m-6-n.

$$m^{2}-6m-mn-6m+36+6n+nm-6n-n^{2}$$

Combine -6m and -6m to get -12m.

$$m^{2}-12m-mn+36+6n+nm-6n-n^{2}$$

Combine -mn and nm to get 0.

$$m^{2}-12m+36+6n-6n-n^{2}$$

Combine 6n and -6n to get 0.

$$m^{2}-12m+36-n^{2}$$