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if (1+x+x^2)^(10)(1-x+x^2)^(10)=a0+ax+a2...

if `(1+x+x^2)^(10)(1-x+x^2)^(10)=a_0+a_x+a_2x^2+a_3x^3+...........+a_(40)x^(40)` then `a_1+a_3+.....+a_(39)` is equal to

A

0

B

`(3^(10)-1)/(2)`

C

`3^(10)`

D

`4^(10)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `(1+x+x^(2))^(10)(1-x+x^(2))^(10)`
`=a_(0)+a_(1)x+a_(2)x^(2)+ . . .+a_(40)x^(40)`.
It can be seen that the expansion does not contain any term containing odd power.
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