How can I whiten my tile floors?

https://homeguides.sfgate.com/use-vinegar-cleaning-porcelain-tile-floors-30205.html

Hydrogen Peroxide.

use bleach, not vinegar on ceramic/porcelain tile

Chlorine Bleach is extremely hard to get its residue “up” and I would try some other options.

You may have a wax build-up and there are wax-stripping products. Although ceramic tile is not to be waxed - so don’t re-wax it later.

Ceramic tile can’t be lightened, but it can be cleaned. First would use a clear-colored pine cleaner, like Pinalen and then I would use TSP. Wear long vinyl gloves and eye protection. Kitchens have a lot of cooking vapors residue everywhere.

Grout can be cleaned and then bleached with an oxygenated powdered bleach solution, like Oxy Clean. This is tedious work with a bent toothbrush & lots of clean water and rags. But the grout always gets dirty.

Grout Cleaner or Food grade hydrogen peroxide may be needed to bleach some grout stains. Be careful, as FG hydrogen peroxide is caustic at full strength and must be diluted to about 7%.

When done, invest in non-yellowing grout sealer to protect your hard work.

Patsy,. Try cleaning just the grout first. Buy grout cleaner, then wash the floor with hand soap. Just a little, that's all you need. Aloha!