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1. I would hide behind the door, listen, and learn the poems on my own.
2. I would hide behind the door listening to and learning the poems on my own.
3. I would hide behind the door listening and learning the poems on my own.
The difference is that the structure of the sentence makes the preposition necessary or not. In 1, it is simply not linked to the poems except through the verb 'learn'. If I say, 'Listen', the context makes it clear what I want you to listen to- if I have a tape recorder, then it is that; if you are talking, then I'd like you to be quiet and listen to me. If you say what it is you want to listen to, then add the preposition.
Listen and listen to 
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