$\begin{array}{l}
B = {x^{2009}} - 2009{x^{2008}} + 2009{x^{2007}} - .... + 2009x - 1\\
Ta\,\,co:\,\,\,x = 2008\\
\Leftrightarrow 2009 = 2008 + 1 = x + 1\\
\Rightarrow B = {x^{2009}} - \left( {x + 1} \right){x^{2008}} + \left( {x + 1} \right){x^{2007}} - .... + \left( {x + 1} \right)x - 1\\
= {x^{2009}} - {x^{2009}} - {x^{2008}} + {x^{2008}} + {x^{2007}} - ..... + {x^2} + x - 1\\
= x - 1 = 2008 - 1 = 2007.
\end{array}$
