This paper develops a general equilibrium model of multi-product firms and analyzes their behavior during trade liberalization. Firm productivity in a given product is modeled as a combination of firm-level "ability" and firmproduct-level "expertise", both of which are stochastic and unknown prior to the firm's payment of a sunk cost of entry. Higher firm-level ability raises a firm's productivity across all products, which induces a positive correlation between a firm's intensive (output per product) and extensive (number of products) margins. Trade liberalization fosters productivity growth within and across firms and in aggregate by inducing firms to shed marginally productive products and forcing the lowest-productivity firms to exit. Though exporters produce a smaller range of products after liberalization, they increase the share of products sold abroad as well as exports per product. All of these adjustments are shown to be relatively more pronounced in countries' comparative advantage industries.