> If they do know, and you tell them, then you've only really confirmed what they already knew.

Not necessarily. This opens you up to accusations of engaging in "mansplaining" which has broadened in definition over the years.

In addition to this, it opens you up to being thought of as a "know it all".

It's far safer, as far as office politics are concerned, to put on your coworkers the burden of asking you to clarify/explain/teach.

Would asking them if they already know or would like something explained be the best thing to do (rather than assuming one way or the other)?