You know what I would do,
Depending on your resources,
Bleach, which I believe is Sodium Hypochlorate (NaClO), can be tested (with your chemistry teacher) in a variety of different ways , but I'll let you find those on your own. Just be careful though, some tests can be dangerous (chlorine=yuck). Then once you have "proven" that tide bleach is a solution of Sodium Hypochlorate (if it is, I'm just assuming), do a little research on why the structure allows bleach to remove stains, and maybe even give some history of "Eau de Javel". That's what I would do.
...but I'm only 16 so,
Good Luck!