I multiplyed x^2-2x+2 times x^2+2x+2. The book suggested the order this be done in as: x^2(x^2-2x+2) then 2x(x^2-2x+2) then 2(x^2-2x+2), with the result being x^4+4. However, I wondered if this could be done in reverse. So I multiplyed x^2(x^2+2x+2), then -2x(x^2+2x=2) then 2(x^2+2x+2). The result however was different. I'm not sure if it was just a computational error or if you really can't do it this way. If you can only do it the first way, why? Thanks!!!
x^4+4 is correct, and should be the same in both ways.
Try it again, and if the result is still different, post your working and we will try to help you find the error.