a) The like terms in the expression 2x^3y+2xy^2+4x^2y^2-2xy are:
2x^3y and 2xy^2 are like terms because they both have the same variables raised to the same powers (x^3 and y) and the same coefficient (2).
4x^2y^2 and -2xy are not like terms because they have different variables (x^2y^2 and xy) and different coefficients (4 and -2).

b) The like terms in the expression x^3-x+3x^2y+3xy^2+y^3-y are:
x^3 and -x are like terms because they both have the same variable raised to the same power (x^3) and different coefficients (1 and -1).
3x^2y and 3xy^2 are like terms because they both have the same variables raised to the same powers (x^2y and xy^2) and the same coefficient (3).
y^3 and -y are like terms because they both have the same variable raised to the same power (y^3) and different coefficients (1 and -1).

c) The like terms in the expression x^2-x-y^2-y are:
x^2 and -x are like terms because they both have the same variable raised to the same power (x^2) and different coefficients (1 and -1).
-y^2 and -y are like terms because they both have the same variable raised to the same power (y^2 and y) and different coefficients (-1 and -1).