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^(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)

Sure! Let's check your answers.

1) For (x+y)^3, you correctly applied the binomial expansion formula. The expanded form is:
(x+y)^3 = x^3+3x^2y+3xy^2+y^3

So, your answer x^3+3x^2y+3xy^2+y^3 is correct!

2) For [x^(3/2)][x+x^(5/2)-x^2], let's simplify it:
= x^(3/2) * (x+x^(5/2)) - x^(3/2) * x^2
= x^(3/2) * x + x^(3/2) * x^(5/2) - x^(3/2) * x^2
= x^(5/2) + x^(8/2) - x^(7/2)

Oops, you made a mistake in the last term. When adding exponents, you need to keep the same base. In this case, it should be - x^(7/2), not - x^(5/2 + 2) = - x^(7/2).

So, the correct answer is: x^(5/2) + x^(8/2) - x^(7/2).

Keep in mind that simplifying and expanding expressions involve basic algebraic operations such as multiplication and addition, as well as understanding the exponent rules. It's always a good idea to double-check any calculations to ensure accuracy.