Question

What is the 5th term of `(x+2)^9`?

Answer 1

`2016x^5`

Explanation:

From the binomial theorem, the term in position `r+1` of the binomial expansion `(x+y)^n=sum_(r=0)^oo ~^nC_rx^(n-r)y^r` is given by

`T_(r+1)= ~^nC_rx^(n-r)y^r`.

Hence `T_5=T_(4+1)=~^9C_4x^(9-4)*2^4`

`=(9!)/((9-4)!4!)*x^5*16`

`=2016x^5`