# How to use r curly brackets only for a part of an equation?

So given the following MWE I wish to align the two equations i.e., the term (A-B) to be in alignment with the terms of alpha but I did not manage to do this with the right curly bracket being present only on top.

How can I manage to do so?

\begin{equation*}
\left.
\begin{aligned}
\alpha = \  & (a + b + c) & \times \\
& (f + g + h) & \times \\
& (w + x + y)
\end{aligned}\right\} \text{first part of eq} \\
\end{equation*}
\begin{equation*}
(A-B) % I want this to be aligned with the rest
\end{equation*}


\begin{aligned} \alpha = \ & (a + b + c) & \times \\ & (f + g + h) & \times \\ & (w + x + y) & \\ & (A-B) & \end{aligned} \begin{aligned} \left. \begin{aligned} & \\ & \\ & \\ \end{aligned}\right\} \text{first part of eq}\\ & \end{aligned}