Let $\{a_i\}_{i=1}^n$ and $\{b_i\}_{i=1}^n$ be sequences of real numbers. Is there a simple formula to expand:
\begin{equation*} \prod_{i=1}^n(a_i+b_i) \end{equation*}
To get a sense of the type of formula I want, consider:
\begin{equation*} (\sum_{i=1}^na_i)^2 = \sum_{i=1}^n a_i^2 + 2\sum_{i=1}^n \sum_{j=1}^{i-1}a_ia_j \end{equation*}
I attempted to expand the product but I am not getting satisfactory results organized in a way that is simple enough to use.