Question

二项式(

x

2

-

1

3 x

)8的展开式中常数项为______．

Answer 1

(

x

2

-

1

3 x

)8展开式的通项是Tr+1=

C

r8

(

x

2

)8-r(-

1

3 x

)r=(

1

2

)8-r(-

1

3

)r

C

r8

x8-

4r

3

令8-

4r

3

=0解得r=6
故展开式的常数项为(

1

2

)2(-

1

3

)6

C

68

=7
故答案为7