\[25a^{2} - (a + 3)^{2} =\]
\[= \left( 5a - (a + 3) \right)\left( 5a + (a + 3) \right) =\]
\[= (5a - a - 3) \cdot (5a + a + 3) =\]
\[= (4a - 3)(6a + 3) =\]
\[= 3 \cdot (4a - 3)(2a + 1)\]