binomial theorem

11th term | (3 x-1/2 y^2)^15 | in lexicographic order

=(729729 x^5 y^20)/1024

EXPANDED:

14348907 x^15-(71744535 x^14 y^2)/2+(167403915 x^13 y^4)/4-(241805655 x^12 y^6)/8+(241805655 x^11 y^8)/16-(177324147 x^10 y^10)/32+(98513415 x^9 y^12)/64-(42220035 x^8 y^14)/128+(14073345 x^7 y^16)/256-(3648645 x^6 y^18)/512+(729729 x^5 y^20)/1024-(110565 x^4 y^22)/2048+(12285 x^3 y^24)/4096-(945 x^2 y^26)/8192+(45 x y^28)/16384-y^30/32768.

SEE HERE: http://www.wolframalpha.com/input/?i=11th+term+of+(3x-1%2F2y%5E2)%5E15

(3x-1/2y^2)^15    .....the 11th term is given by :

C(15, 10)  * (3x)^5 * [(-1/2) y^2]^10   =

3003 * (243) *x^5  * (1024)y^20  =

[3003 * 243] / 1024 * x^5 * y*20  =

729,729/ 1024 * x^5 * y^20