\[\left( 4ab - b^{2} \right) + 2 \cdot (a - b)^{2} =\]
\[= 4ab - b^{2} + 2 \cdot \left( a^{2} - 2ab + b^{2} \right) =\]
\[= 4ab - b^{2} + 2a^{2} - 4ab + 2b^{2} =\]
\[= 2a^{2} + b^{2}.\]