show interest 与 be interested in 与 become interested in 与 ta

show interest 表示对...表现出兴趣,如She shows interest in the love story.
be interested in表示一种状态,就是对...有兴趣I'm interested in reading.
become interested in强调动作,就是变得对...有兴趣When I grow up,I become interested in collecting stamps.
take an interest in =become interested in即对...有兴趣,如When he was a boy,she took an interest in sience.