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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply -4 by m+n-1.

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

Expand

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

Solution Steps

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

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

Use the distributive property to multiply -4 by m+n-1.

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