Oxidation of the plastic lens of car headlights reduces the distance the headlights light up the road. Replacement of these headlights can be very expensive, but repair is easy and inexpensive using materials you already have in your house.
Wet a small cloth, such as a face cloth and wring out until it is just damp. Fold it to a square about 4 inches across.
Squeeze a ribbon of toothpaste onto the folded cloth.
Rub the toothpaste on the surface of the headlight. If the headlight is badly yellowed you may need to rub for several minutes, rinsing the cloth and applying more toothpaste as needed.
Rinse the toothpaste from the headlight surface.
Be patient. Cleaning the yellowing from a headlight can take a lot of rubbing. The headlight shown in this article was badly yellowed, but cleaned up in about 15 minutes.