Explanation

Each factor contributes one chosen symbol, so a term with exactly one x takes x from exactly one factor and y from the other nine. Taking x1 from the first factor gives 1 way and forces y elsewhere; taking −y1 from the first factor lets the single x come from any one of the remaining nine factors (9 ways). That gives 1 + 9 = 10 such terms. The option 2¹⁰ counts all terms, and 20 double-counts. Hence the answer is 10.