An apple core given to your chickens is a great way to reduce waste, but it won't much affect your feed bill. Apples are a tasty treat, but too low in protein to help affect your feed bill much. You can also feed other kitchen scraps, but limit the scraps to no more than 10-20% of their total daily diet. Most scraps are low protein, which is why you want to limit it. Unless, of course, you are feeding them leftover meatloaf, pork chops, fish, etc, ideally with little to no salt.
Also, Apple seeds are somehwt toxic. For humans, I beleive you need to eat at least 2 cups of pure Apple seeds to reach toxic levels. Not sure how that equates for chickens, but an apple core here or there for several birds isn't going to hurt them any. In fact, some folks beleive that while the poison in Apple seeds are toxic in great quantities, they can be immune system stimulating in small amounts.