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What is the coefficient of the middle te...

What is the coefficient of the middle term in the binomial expansion of `(2+3x)^(4)`?

A

6

B

12

C

108

D

216

Text Solution

Verified by Experts

The correct Answer is:
D
Middle term in the expansion of `(x + y)^(n)`
`=((n+1)/(2))^(th)` term, if n is odd
`=((n)/(2)+1)^(th)` term, if n is even
Here n = 4
`therefore` Middle term is `((4)/(2)+1)^(th)=3^(rd)` term
`4c_(2) xx 2^(2) xx 3^(2) = 6 xx 4 xx 9 = 216`
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