Find the middle term in the expansion of :
(i) (3 + x)6
(ii) 
(iii) 
(iv) 
(i) For (3 + x)6,
a=3, b=x and n=6
As n is even, 
is the middle term
Therefore, the middle term 
General term tr+1 is given by,
Therefore, for 4th , r=3
Therefore, the middle term is
= (20). (27) x3
= 540 x3
(ii) For 
,
, b=3y and n=8
As n is even, 
is the middle term
Therefore, the middle term 
General term tr+1 is given by,
Therefore, for 5th , r=4
Therefore, the middle term is
= (70). x4 y4
(iii) For 
,
, 
and n=10
As n is even, 
is the middle term
Therefore, the middle term 
General term tr+1 is given by,
Therefore, for 6th , r=5
Therefore, the middle term is
= -252
(iv) For 
,
a=x2, 
and n=10
As n is even, 
is the middle term
Therefore, the middle term 
General term tr+1 is given by,
Therefore, for the 6th middle term, r=5
Therefore, the middle term is
= -252 (32) x5
= -8064 x5