數學知識交流---(x+y)^30

Expand (x+y)^30:

(x+y)^30
= (x+y)(x+y)(x+y)(x+y)(x+y)(x+y)...
= x^30 +
30 x^29 y +
435 x^28 y^2 +
4060 x^27 y^3 +
27405 x^26 y^4 +
142506 x^25 y^5 +
593775 x^24 y^6 +
2035800 x^23 y^7 +
5852925 x^22 y^8 +
14307150 x^21 y^9 +
30045015 x^20 y^10 +
54627300 x^19 y^11 +
86493225 x^18 y^12 +
119759850 x^17 y^13 +
145422675 x^16 y^14 +
155117520 x^15 y^15 +
145422675 x^14 y^16 +
119759850 x^13 y^17 +
86493225 x^12 y^18 +
54627300 x^11 y^19 +
30045015 x^10 y^20 +
14307150 x^9 y^21 +
5852925 x^8 y^22 +
2035800 x^7 y^23 +
593775 x^6 y^24 +
142506 x^5 y^25 +
27405 x^4 y^26 +
4060 x^3 y^27 +
435 x^2 y^28 +
30 x y^29 +
y^30

^係咪解x
如是:(x+y)^30
=(x^30)+(y^30)
=30x+30y

2011-11-13 22:17:50 補充：
(x+y)(x+y)...(x+y)
=x 30次方+30xy+y 30次方