Solve (m-1)^2-2m(m-1)+m^2-4

$$( m - 1 ) ^ { 2 } - 2 m ( m - 1 ) + m ^ { 2 } - 4$$

Evaluate

$$-3$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-1\right)^{2}.

$$m^{2}-2m+1-2m\left(m-1\right)+m^{2}-4$$

Use the distributive property to multiply -2m by m-1.

$$m^{2}-2m+1-2m^{2}+2m+m^{2}-4$$

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

$$-m^{2}-2m+1+2m+m^{2}-4$$

Combine -2m and 2m to get 0.

$$-m^{2}+1+m^{2}-4$$

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

$$1-4$$

Subtract 4 from 1 to get -3.

$$-3$$

Factor

$$-3$$