\[(b - 3)(b - 4) - (b + 4)^{2} =\]
\[= b^{2} - 4b - 3b + 12 - \left( b^{2} + 8b + 16 \right) =\]
\[= b^{2} - 7b + 12 - \ b^{2} - 8b - 16 =\]
\[= - 15b - 4\]