\[b^{6} - 4b^{4} + 12b^{2} - 9 =\]
\[= b^{6} - \left( 2b^{2} - 3 \right)^{2} =\]
\[= \left( b^{3} - 2b^{2} + 3 \right)\left( b^{3} + 2b^{2} - 3 \right)\]