Hi,
Thank you so much for your reply.
Woow! Very interesting! Is it because when you use the verb 'feed' it is understood that it is by, in this case, themselves. That's why you don't need the preposition.
No, your explanation can't be right, because it's 'by' that is omitted, not "themselves". Both sentences have 'themselves' in them, so it not 'understood.'
Consider the following:
1. The children feed the cats themselves. (The children, themselves, feed the cats. We don't)
2. The children feed the cats by themselves. (The children don't need our help to feed the cats.)
3. The children eat by themselves. (The children don't need our help to eat or to feed themselves.)
4. The children eat themselves. (The children are autophagous).
Do you understand these sentences?
PS: The addition of "can" makes another change. If you want to know the difference between two sentences, you should keep the difference to one variable - unless you have two actual sentences that you can't tell apart.