Can I write these sentences as shown below?
We aren't at home. We're not at home
I'm not busy. I am not busy.
With an explanation, please.
Yes, you can.
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Sorry, I overlooked the last line.
We aren't at home. We're not at home. Both forms are OK. To my mind, We're not at home is a litttle more emphatic, probably because you are saying the word 'not' fully.
I'm not busy. I am not busy. You don't have to use contractions. In fact, in formal English you shouldn't use them.
Clive