Question

Find the middle term (s) in the expansion of
1
i) (3x + 7y)10
ii) 3x +1/
2ypower 4​

Answer 1

• To find :- Middle term in the expansion of (1+3x+3x2+x3)2n.

solution :- 

(1+3x+3x2+x3)2n=[(1+x)3]2n    (∵ we know (a+b)3=a3+b3+3a2b+3ab2)

=(1+x)6n

Here Power =6n=2(3n)=even

Here Total no. of terms are odd.

So, There are only one middle term 

i.e. (26n)th term=(3n)th term

T3n is to be find now,

we know formula for general term.

Tr+1=nCrxn−r.yr in expansion of (x+y)n.

T3n=6nC(3n−1)x(3n−1)⟺ final answer