Now if and , the only terms that have integer values are when and are even. (Note that , but the only way this combines with other even powers is in the term ; i.e. where .)
- if , and there are 4 possible choices
- if , and there are 3 possible choices
- if : 2 choices
- if : 1 choice
Total number of terms, then, is 4+3+2+1 = 10. Answer: D.