Idiom: "Хлопот полон рот" or "хлопот полный рот"?

Question

This idiom roughly translates as "the thing is, he/she is very busy", right?

However, a friend of mine on VK used "Хлопот полный рот", whereas on gramota.ru I saw "хлопот полон рот". Which one is correct, or are they both correct?

Answer 1

"Полон" is the short form of "полный" and in this case they are absolutely interchangeable. However, "хлопот полон рот" is more euphonic and thus it is the preferable one.

Answer 2

This idiom roughly translates as "the thing is, he/she is very busy", right?

Right.

Хлопот полон рот is the correct one, but both are perfectly understandable.

Answer 3

Хлопот полон рот is idiomatic; хлопот полный рот is — well, like saying "shiver my timbers" instead of the more iconic "shiver me timbers". Полон is a bit of a relic here, from a time when short adjectives were more generally "indefinite", something like the Germanic weak adjective, instead of the more narrow predicative function ("is full") that they have today.