\[b^{10} - 25b^{8} - 40b^{4} - 16 =\]
\[= b^{10} - \left( 25b^{8} + 40b^{4} + 16 \right) =\]
\[= b^{10} - \left( 5b^{4} + 4 \right)^{2} =\]
\[= (b^{5} - 5b^{4} - 4)(b^{5} + 5b^{4} + 4)\]