I would like to know if there is a sum-of-products expansion for the following product-of-sums. A special case is given here for the difference of two entries.
$$\prod_{j=1}^{n} \left( \sum_{i= 1}^{m} x_{i, j} \right)$$
I suspect the result will be a sum-of-product-of-products because of having to distribute each term of each factor out to each term of each other factor.