To add two polynomials, you just put them together. For example, if you had to add −2x2 + 4y2 − 2y and −xy2 + 3x2 − x, the first step is just to write them as one polynomial, getting −2x2 + 4y2 − 2y − xy2 + 3x2 − x. (In this case, the second polynomial started with a minus sign; if it hadn't, then we would have put a plus sign in between.) Now we have to collect like terms. The only two terms we can combine are the −2x2 and the + 3x2. They combine to x2, since −2 + 3 = 1 and 1x2 is the same thing as x2. So the answer is x2 + 4y2 − 2y − xy2 − x.
If we had to subtract the polynomials instead of adding them, then we would do almost the same thing, except we would switch the signs of all the terms of the second polynomial. (Be sure to switch all of them.) Then we would get −2x2 + 4y2 − 2y + xy2 − 3x2 + x. We still need to collect like terms, though, so we would end up with −5x2 + 4y2 − 2y + xy2 + x.
Note that these are all still polynomials, even though they have more than one letter in them.