Statistics and Probability question

Let X be a random variable. By expanding the expression E(X^2-E(X))^2 show
that E(X^2) > (E(X))^2.

Are you sure that you are expending E(X^2-E(X))^2 and not E(X - E(X))^2 ?
note that 0<= E(X - E(X))^2 = E( X^2 - 2XE(X) + (E(X))^2 = E(X^2) - 2(E(X))^2 + (E(X))^2 =
E(X^2) - 2(E(X))^2
Thus E(X^2) - 2(E(X))^2 >= 0, or E(X^2) > = (E(X))^2.