Europe this month rolled out new restrictions on makers of chemicals linked to cancer and other health problems, changes that are forcing U.S. industries to find new ways to produce a wide range of everyday products.

The new laws in the European Union require companies to demonstrate that a chemical is safe before it enters commerce -- the opposite of policies in the United States, where regulators must prove that a chemical is harmful before it can be restricted or removed from the market. Manufacturers say that complying with the European laws will add billions to their costs, possibly driving up prices of some products.