\[( - a)^{2n + 1} = ( - 1 \cdot a)^{2n + 1} =\]
\[= ( - 1)^{2n + 1} \cdot a^{2n + 1} =\]
\[= - 1 \cdot a^{2n + 1} = - a^{2n + 1}.\]