Here are my answers. Can you check if I got the right answers? Thank you!
(x+y)^3= x^3+3x^2y+3xy^2+y^3
[x^(3/2)][x+x^(5/2)-x^2]
= x^(5/2)+x^4-x^(3/2)
the last term in the second question should be - x^(7/2), (you were adding 5/2 and 2 in the exponents)