Question

Find the middle term in the expansion of (a/2+x/6)^8

Answer 1

Here No. of terms will be 9 and so, Middle term = 5th term...
So I stopped calculation after 5th term....
In case, you need to calculate further, USE BINOMIAL THEOREM

Answer 2

Hey there !!!

n/2+1th term is the middle term of a binomial expansion of the form (X+Y)ⁿ where n is even .
So, 8/2+1=5th term is middle term of given binomial exapansion.

So, now general term of a binomial expansion  (x+y)ⁿ  is nCr(X)^n-r(Y)^r
here n=8 r=4 X=a/2 Y=x/6
                     =8C₄(a/2)⁴(x/6)⁴

                   =70*a⁴*x⁴/2⁴*6⁴
                   =70a⁴x⁴/16*36*36
                   =35a⁴x⁴/10368

HOPE THIS HELPED YOU !!