be interested in 意思是对...有兴趣 I'm interested in reading.这里interested是adj.
show interest 表示对...表现出兴趣,这里interest是名词,如She shows interest in the love story.
interest sb in sth,这里interest 是动词,意思是某事在某方面引起了某人的兴趣.The book interests Tom in its age.