Solve (10-m)^2-(m-2)^2

$$( 10 - m ) ^ { 2 } - ( m - 2 ) ^ { 2 }$$

Evaluate

$$96-16m$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10-m\right)^{2}.

$$100-20m+m^{2}-\left(m-2\right)^{2}$$

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

$$100-20m+m^{2}-\left(m^{2}-4m+4\right)$$

To find the opposite of m^{2}-4m+4, find the opposite of each term.

$$100-20m+m^{2}-m^{2}+4m-4$$

Combine m^{2} and -m^{2} to get 0.

$$100-20m+4m-4$$

Combine -20m and 4m to get -16m.

$$100-16m-4$$

Subtract 4 from 100 to get 96.

$$96-16m$$

Expand

$$96-16m$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10-m\right)^{2}.

$$100-20m+m^{2}-\left(m-2\right)^{2}$$

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

$$100-20m+m^{2}-\left(m^{2}-4m+4\right)$$

To find the opposite of m^{2}-4m+4, find the opposite of each term.

$$100-20m+m^{2}-m^{2}+4m-4$$

Combine m^{2} and -m^{2} to get 0.

$$100-20m+4m-4$$

Combine -20m and 4m to get -16m.

$$100-16m-4$$

Subtract 4 from 100 to get 96.

$$96-16m$$