"Homework is hard."
たいへん means hard in the sense of being hard work, rather than it necessarily being difficult.
Yeah. I had always know taihen as "difficult situation" not a synonym for "muzukashi". :/
They are synonyms though, as in they both mean difficult/hard. I'd say たいへん has more of a complaint connotation to it (kinda like めんどくさい), whereas むずかしい is more of a simple neutral statement. But that may also be contextual and/or just depending on intonation.
Well, they're similar, but not to the extent I'd call them synonyms. In English, "hard" can be used to mean "difficult", but that too is contextual. E.g. if you're talking about something that is "not soft", you can't say it's difficult. The same goes for むずかしい and たいへん; they can have the same function, but aren't interchangeable.
Like you said, たいへん carries more judgement; a situation you find awful/severe, and clearly negative, while むずかしい is something complicated/serious, but a little more 'neutral'.
Ok, I understand why たいへん can mean hard, but why is むずかしい wrong here? Does "しゅくだいはむずかしいです" not mean the same thing?
Muzukashii should be accepted here, just have to wait for our suggestions to get through to the powers that be.
Sorry, I didn’t get that from what he said at all, thanks for clarifying. Of course the nuance is different, we just can’t know which nuance is expected without context.