You may want to review multiplying polynomials by monomials first.
Multiplying polynomials can take a long time. Suppose you have to multiply x3 − x2 − 1 by x4 − x + 2. Then you need to multiply each term of the first one by each term of the second. Since in this case our two polynomials each have three terms, you'll have to do a total of 3 * 3 = 9 multiplications. To keep the signs straight, I recommend keeping the minus signs with the terms. Here we go.
Now, we put it all together. Remember that, just like with adding polynomials, we put a plus sign if there's no minus sign. So we get x7 − x4 + 2x3 − x6 + x3 − 2x2 − x4 + x − 2. Finally, we collect like terms, so our answer is x7 − 2x4 + 3x3 − x6 − 2x2 + x − 2. (We could rearrange this so the exponents would be in descending order, but you don't have to.)