Solve (5m-m)^2-(m+n)^2

$$( 5 m - m ) ^ { 2 } - ( m + n ) ^ { 2 }$$

Evaluate

$$\left(3m-n\right)\left(5m+n\right)$$

Solution Steps

Combine 5m and -m to get 4m.

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

Expand \left(4m\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$16m^{2}-\left(m+n\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+n\right)^{2}.

$$16m^{2}-\left(m^{2}+2mn+n^{2}\right)$$

To find the opposite of m^{2}+2mn+n^{2}, find the opposite of each term.

$$16m^{2}-m^{2}-2mn-n^{2}$$

Combine 16m^{2} and -m^{2} to get 15m^{2}.

$$15m^{2}-2mn-n^{2}$$

Expand

$$15m^{2}-2mn-n^{2}$$

Solution Steps

Combine 5m and -m to get 4m.

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

Expand \left(4m\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$16m^{2}-\left(m+n\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+n\right)^{2}.

$$16m^{2}-\left(m^{2}+2mn+n^{2}\right)$$

To find the opposite of m^{2}+2mn+n^{2}, find the opposite of each term.

$$16m^{2}-m^{2}-2mn-n^{2}$$

Combine 16m^{2} and -m^{2} to get 15m^{2}.

$$15m^{2}-2mn-n^{2}$$