\[c(c - 2)(c + 2) - (c - 1)\left( c^{2} + c + 1 \right) =\]
\[= c\left( c^{2} - 4 \right) - \left( c^{3} - 1 \right) =\]
\[= c^{3} - 4c - c^{3} + 1 = - 4c + 1.\]