Learn Portuguese (Portugal): O rapaz foi mal-educado com a professora.

It literally translates to 'badly brought up' or 'badly raised'. In Portuguese, this is the standard way to say someone is 'rude' or 'impolite'. To talk about someone's academic schooling, you would use a word like instruído.

Why do we use foi (from ser) here instead of a temporary verb?

This is a tricky aspect of ser versus estar. Using foi describes the nature of the event itself—his action was a rude one. You could say esteve to emphasize he was acting completely out of character for a short time, but foi is much more common for describing an incident that happened.

The translation says 'rude to', so why does the Portuguese sentence use com?

When describing a behavior or attitude directed at another person (like being rude, nice, angry, or careful), Portuguese uses the preposition com (with). Literally, he was rude 'with' the teacher.

How does the word mal-educado change if the sentence is about a girl?

Only the second half of this compound word changes to match gender and number. The word mal is an adverb and never changes. So, for a girl, it becomes mal-educada, and for a group, it would be mal-educados or mal-educadas.