If `(1+2x+x^2)^n=sum_(r=0)^(2n)a_r x^r ,then a=` `(^n C_2)^2` b. `^n C_rdot^n C_(r+1)` c. `^2n C_r` d. `^2n C_(r+1)`

Options

A. `(.^(n)C_(r))^(2)`
B. `.^(n)C_(r)..^(n)C_(r+1)`
C. `.^(2n)C_(r)`
D. `.^(2n)C_(r+1)`

Answer

C

Explanation

`(1+2x+x^(2))^(n)=underset(r=0)overset(2n)suma_(r)x^(r)`
or `[(1+x)^(2)]^(n)=underset(r=0)overset(2n)suma_(r)x^(n)`
or `(1+x)^(2n) = underset(r=0)overset(2n)suma_(r)x^(r)`
`underset(r=0)overset(2n)sum.^(2n)C_(r)x^(r) = underset(r=0)overset(2n)suma_(r)x^(r)`
or `a_(r) = .^(2n)C_(r)`