\[(4x - 3)^{2} - 25 =\]
\[= (4x - 3 - 5)(4x - 3 + 5) =\]
\[= (4x - 8)(4x + 2) =\]
\[= 4 \cdot (x - 2) \cdot 2 \cdot (2x + 1) =\]
\[= 8 \cdot (x - 2)(2x + 1)\]