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