enlarge, extend

拡張(かくちょう)	To extend or physically enlarge a thing (an extended family, enlarge the factory).

広げる(ひろげる)	To spread or widen (to spread a blanket on a bed, to widen a street, open one’s arms). Like the related term 拡張, but 広げる is only in 2 dimensions, I guess. $$$

拡げる(ひろげる)	To spread or extend... 90% the same as regular 広げる. BUT, 拡げる-with-aー手 has one special meaning which 広げる-with-noー手 does NOT have:to expand your markets overseas, to expand your territory, to expand the circulation of your newspaper.

拡大(かくだい)	More formal than 拡張:Literally it means to zoom in on or magnify. Figuratively it means to escalate (a conflict) or scale-up (a buildup of some sort)