\[3b^{2} - 12b + 11 =\]
\[= 3 \cdot \left( b^{2} - 4b + \frac{11}{3} \right) =\]
\[= 3 \cdot \left( b^{2} - 4b + 4 - \frac{1}{3} \right) =\]
\[= 3 \cdot (b - 2)^{2} - 1\]