I would try out different numbers. You are correct for the first question that you are comparing y^8 and y^16. However, try y = 0 and y = 2 for example to see if they differ.
Similarly, (x+y)^4 requires foiling out (x+y)(x+y)(x+y)(x+y). Instead of doing that, choose a few pairs of possible x and y values to test. Compare (x+y)^4 to x^4 x y^4 when x= 0 and y =0 and when x = 1 and y = 1 for example.