\[(c + 7)c - (1 - c)^{2} =\]
\[= c^{2} + 7c - \left( 1 - 2c + c^{2} \right) =\]
\[= c^{2} + 7c - 1 + 2c - c^{2} =\]
\[= 9c - 1.\]