\[(a + b)b - \left( a^{2} + b^{2} \right)(a - 2) =\]
\[= ab + b^{2} - a^{3} - ab^{2} + 2a^{2} + 2b^{2} =\]
\[= - a^{3} - ab^{2} + 2a^{2} + 3b^{2} + ab.\]