What is the right way of asking someone to give a more detailed explanation of what he just said (or wrote)?

Question

I was told something and now I want to get a more detailed explanation of what the person just said (or wrote).

For example, the person wrote to me:

The key difference between the two definitions is that valid is a property of sentences and satisfiable is a property of sets of sentences.

Now I want to get that sentence to be explained in more detail to me.

I answered:

Can you please elaborate?

Link to that conversation: https://www.reddit.com/r/logic/comments/99geaz/satisfiability_and_validity/e4nyate/

Questions:

1. Is this the right way of asking someone to give a more detailed explanation of what he just said (or wrote)?
2. What are other ways (maybe better, maybe just other) of asking someone to give a more detailed explanation of what he just said (or wrote)?
3. Is there a difference when we speak and when we write? I mean, maybe some variant is better to use when we speak and some is better when we write?

If there is a difference between American English and British English regarding that topic please write that too.

Answer 1

elaborate is OK, but it's quite formal. Note that elaborate is intransitive: if you want to specify a subject, you have to use the preposition on.

One possibility is to use the phrasal verb expand on.

Can you please expand on that?

According to this NGram graph, this phrasal verb is equally common in the US and UK.