I'm pretty much stuck on these problems and don't know where to start on several of them.
5.30: Don't know where to start besides plugging in the x values and trying to bash or find something helpful. 

5.31: I factored this into (x+2y)(x-2y)(x+y)(x-y)(x+3y). From there, I tried to do different cases where x and y were even and odd. It is easy to prove all cases except x being odd and y being even because there are always factors of 2 in the expression. I don't really know how to solidly prove that the expression is not divisible by 33 when x is odd and y is even besides plugging in values.

5.32: This looks a bit like some theorem or identity but I can't remember off the top of my head, so I don't really know where to start. 

5.33: I also don't really know where to start on this question. 

I would appreciate it if you could just give me a place to start for the questions that I don't know and a way to solidly prove the question that I partially know how to do.