如果(3x?x)n的展开式中二项式系数之和为128,则展开式中x4的系数是(  )A.7B.-7C.-21D.2

2025-04-23 03:09:37
推荐回答(1个)
回答1:

C
+
C
+…+
C
=2n=128=27
∴n=7.
∴Tr+1=
C
?(3x)7-r?(?x
1
2
)
r
=(-1)r?37-r?
C
?x7?r+
r
2

∴由7-
r
2
=4得r=6.
∴展开式中x4的系数是:3
C
=21.
故选D.