I could not find a video on youtube that addresses this parenthesis issue. Maybe I was not using the correct keyword.
However, is there any differences between ∃x(∀yP(x,y)) and ∃x∀yP(x,y).
Sorry for writing a short question. I don't want to extend it necessarily.
There is no difference. The parentheses are used to make the nesting of the quantifiers more explicit, they are excluded to make the expression easier to write (and possibly to read as well).
It is similar to how, once we have established that $(a + b) + c = a + (b + c)$, we will just write $a + b + c$.