\[a^{6} + a^{4} - 3a^{2} - 3 =\]
\[= a^{4}\left( a^{2} + 1 \right) - 3 \cdot \left( a^{2} + 1 \right) =\]
\(= \left( a^{2} + 1 \right)\left( a^{4} - 3 \right)\)