\[3p(p - 5) - (p - 4)(p + 8) =\]
\[= 3p^{2} - 15p - \left( p^{2} + 8p - 4p - 32 \right) =\]
\[= 3p^{2} - 15p - p^{2} - 8p + 4p + 32 =\]
\[= 2p^{2} - 19p + 32.\]