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How are they different 'to ask a favor' and 'to ask for a favor'? Do they have different uses or connotations?
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I see all of these as being the same:

Jim, can I ask a favor of you?
Jim, could you please do me a favor?
Jim, could I ask you for a favor?

I don't see any difference in connotation, but "ask a favor of" and "ask for a favor from" is how I use them.
GG,

Interesting. I don't use that third one at all.
I thought we asked someone to do the favor for us, not asked someone for the favor.

I believe I've heard ... for a favor pretty often, though.

CJ
You're right.

But I can hear either of these as being equally likely. East coast thing?

A: Why do you need to talk to Jim?
B: I need to ask him a favor.
or
B: I need to ask him for a favor.