British American Tobacco Plc has agreed to fully take over Reynolds American Inc. on terms that are improved from an initial bid made last year. The takeover would create the world’s largest publicly traded tobacco company and combine BAT’s presence in developing countries, where anti-smoking campaigns are not as strong as in the U.S. and Europe, with Reynolds’ almost exclusive focus on the U.S. BAT said Tuesday it will buy the 57.8 percent of Reynolds it does not already own.