\[\begin{array}{l} {B_n}\left( {1 - x} \right) = {\left( { - 1} \right)^n}{B_n}\left( x \right) \hfill \\ {\left( { - 1} \right)^n}{B_n}\left( { - x} \right) = {B_n}\left( x \right) + n{x^{n - 1}} \hfill \\ \end{array}\]