Learn Hardcore Russian: Повтори это правило ещё раз, пожалуйста.

Повтори is the imperative (command/request) form of the verb повторить (to repeat).
It’s the 2nd person singular imperative, so it’s used when speaking to one person you address as ты (informal).

What’s the difference between Повтори and Повторяй?

They differ mainly by aspect:

Повтори (from повторить, perfective) = repeat it once / do it (to completion) one time. This fits well with ещё раз (one more time).
Повторяй (from повторять, imperfective) = repeat (in general / repeatedly / as a process). It can sound like “keep repeating” or “repeat regularly,” depending on context.

In this sentence, Повтори ... ещё раз is the natural pairing because the request is for one additional repetition.

Is this sentence informal or formal? How do I make it polite to a stranger/teacher?

As written, it’s informal because of Повтори (ты-form).
For formal/polite вы-form, use:

Повторите это правило ещё раз, пожалуйста.

That’s the standard polite version for a teacher, a customer interaction, or someone you don’t know well.

Why is it это правило and not some other case?

Because правило is the direct object of repeat, so it takes the accusative case.
For neuter inanimate nouns like правило, the accusative form looks the same as nominative: правило.

это agrees with правило (neuter singular), so you get это правило.

Can I drop это and just say Повтори правило ещё раз?

Yes. Повтори правило ещё раз, пожалуйста. is grammatical and common.
Including это makes it slightly more specific, like this rule (the one we’re discussing).

What does ещё раз literally mean, and how is it used?

Literally, ещё = still / yet / more, and раз = time (an occurrence).
Together ещё раз means one more time / again.

It’s a fixed, very common phrase used with requests and instructions:

Скажи ещё раз. = Say it again.
Объясните ещё раз. = Explain again.

Is ещё раз the same as снова or опять?

They overlap but aren’t identical:

ещё раз = one more time (explicitly “an additional repetition”)
снова = again (neutral “again”)
опять = again but often with an emotional color like “again… (ugh)” depending on tone/context

In a polite request, ещё раз is especially natural.

Why is there a comma before пожалуйста? Is it required?

Here пожалуйста functions like a parenthetical politeness marker (please), so it’s commonly set off with a comma:

Повтори это правило ещё раз, пожалуйста.

In casual writing people may omit the comma, but in standard punctuation, the comma is preferred.

Where can пожалуйста go in the sentence?

Several positions are possible, with slightly different emphasis:

Пожалуйста, повтори это правило ещё раз. (polite opener)
Повтори это правило, пожалуйста, ещё раз. (please inserted mid-sentence)
Повтори это правило ещё раз, пожалуйста. (common, neutral)

All are acceptable; the last one is very typical in speech.

How do you stress and pronounce the key words?

Common stress patterns:

повторИ (poftorÍ) — stress on the last и
прАвило (PRÁ-vi-la) — stress on А
ещё (yeshYÓ) — stress on ё (the ё is always stressed, even if written as е in many texts)

A simple transliteration: Povtorí eto prá-vilo yeshchó raz, pozhalúysta.