Do they have the same meaning?
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If sentence A has a comma like:
then Sjiveru is right.
However, it doesn't have a comma, so they have the same meaning. They mean "There are many students who go without doing their homework." The して行かない doesn't mean "don't go" but "don't do their homework."
The sentence A:
This almost always means "There are many students who go to school without doing their homework." (ie, they go to school anyway)
In English, "Don't drink and drive" always means "Don't drive after you drink", not "Don't drink! Do drive!". Here "drink-and-drive" is treated as one set. And "Let's not go and see him" does not usually mean "Let's stay home, and let's see him instead."
Quite similarly, in Sentence A, the ない negates "宿題をして行く" part as a whole. That's why it's effectively the same as Sentence B.
Other similar examples:
- 遊んで暮らすな。 Don't live in idleness. (not "Play! And die!")
- 物を口に入れて喋らないでください。 Please don't speak with your month full.
- 物を口に入れて、喋らないでください。 Please fill your mouth with food, and don't speak. (See the comma)
No, they are quite different.
B is fairly normal, and means 'there are many students who go [to school, I assume] without doing their homework'. The doing part is negated, not the going - they still go to school, it's only the homework they don't do.
A can instead be translated as 'there are many students who do their homework and then don't go'. The going is negated, not the doing; the negative doesn't extend over the whole phrase.
Sjiveru is right, but allow me to break it down a bit...
The て part indicates the verb is in te-form ( て形【けい】 in Japanese ). It has many uses which you can review on your own, but the one I want to highlight here is how it connects clauses or verbs together. This can be roughly translate the verb to "and" but also "but" like:
I ate cake and drank coffee.
I didn't eat cake but drank coffee.
So, knowing this, let's look at your two sentences.
There are many students who do their homework but don't go (to school).
There are many students who don't do their homework and go (to school).
In each case, I made the positive statements bold, so you can kind of see what's going on. Does this make sense? If not, let me know.