\[(m - n + 1)(m + n) =\]
\[= m \cdot m + \text{mn} - \text{nm} + n \cdot n + m + n =\]
\[= m^{1 + 1} - n^{1 + 1} + m + n =\]
\[= m^{2} - n^{2} + m + n.\]