\[(a - 4)^{2} + a(a + 8) =\]
\[= a^{2} - 2a \cdot 4 + 4^{2} + a^{2} + 8a =\]
\[= 2a^{2} - 8a + 16 + 8a =\]
\[= 2a^{2} + 1\text{.\ }\]