Related: How did Snape figure out the stuff he had written in his Advanced Potion-Making book?
If Slughorn knew modifications to the potions textbook that would make the potions better, why didn't he tell students about them? If he didn't, why did he seem to expect that it was possible to get better results than the potions they were making? Wouldn't his potions look just like Hermoine's, given that she was following the directions very literally?