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Get them cleaned by the hygienist at the dentist first. It’ll more-permanently remove most of the yellowing and staining up near the gum line which is built up in tartar. You’ll be surprised how much will have built up and what a difference it makes after a scale and polish. Then just use one of those kits from Boots. The iwhite one works well.
I wouldn’t mess around with hydrogen peroxide in a homebrew to be honest. I tried it once by using contact lens solution (around 6% concentration) in a retainer and it ended up bleaching and burning my gums as well. I don’t know how much they put in whitening gel but it can’t be much.
What's the best bang method for buck teeth whitening?
Google says this - Hydrogen peroxide is a mild bleach that can help to whiten stained teeth . For optimal whitening, a person can try brushing with a mix of baking soda and hydrogen peroxide for 1–2 minutes twice a day for a week. They should only do this occasionally.
Sounds reasonable, guess you'd want to be careful to make the correct combination.