If you have hard water, a scoop of Borax will do wonders for the effectiveness of regular detergents.
Your mom’s right about bleach and elastic, but the stuff is OK for occasional use on many whites. It takes a while for fabric to build up a dingey look, so once every ten or so washes should do the job.
Sometimes the cleanest whites will look gray or yellowed, even though they’re spotless. Bleach can’t help you at that point. A “laundry bluing” product will make the the grimy, gray, or yellow undertones disappear and the white looks really whiter and brighter. It’s a blue-rinse that actually DOES deposit some blue onto the white, and makes the white…whiter. Maybe try some out with old socks or a t-shirt to see how it works first. Don’t overdo the measurement they recommend, or the blue will be noticeable.
ISTR that Oxy Clean has a surprisingly low amount of the active ingredient, so you might want to try a similar product from a different company (if you do a web search, you’ll find some pages that rate the different products). I’ve used this stuff and it seemed to work pretty well. Not perfectly, but a heckuva lot than my standard detergent-with-bleach.
In high school, I played football. We had white practice (and game) pants, which would, naturally, get extremely dirty during an average practice, especially as it got later in the fall and there would be more rain and snow. While all my teammates would just wear the pants every practice without washing, my mother wasn’t into it. Every week, after the Friday game, I would bring home all my game clothes to wash. We would soak all my whites (pants, socks, etc) overnight in a bucket of warm water with a healthy dose of Cascade dishwashing powder dissolved into it (I never measured how much I put in, but it was a good amount, and it was into a 5 gallon bucket, so it was probably a pretty high concentration). After a good soaking overnight, we would throw everything into a warm wash with regular detergent. Everything would come out very bright and clean.
Also, the elastic in the socks held up very well, as did the spandex in the tights I wore in cold weather.
OxiClean IS NapiSan, more or less. Both are sodium percarbonate bleaches, with some other stuff. If you’re just not getting enough percarbonate in your wash, you can buy it and add it yourself:
Are they yellow (problem is hard water) or grey (problem is really dirty clothes)?
Soak clothes in room teperature water with detergent and borax; rinse, with borax if the clothes are really dirty.
Re-wash (put do NOT soak) with very warm/hot water and chlorine bleach and borax; rinse with borax; then rinse with Mrs. Stewarts (the only blueing I’ve ever seen in stores).
Do you want a white shirt that looks dingy for a really long time, or a nice new white shirt every year?
On the other hand, do you care if your underwear is very white?