Question

What is the 5th term in the binomial expansion
(a+b)^7

Answer 1

On Apex

Explanation:

35a^4 b^3

Answer 2

5th term is 35a^4b^3

Explanation:

We need to find the 5th term in binomial expansion (a+b)^7

The binomial theorem is:

`(x+y)^n = \sum_(n=0)^(k) {n\choose k}x^ky^(n-k)`

We are given

x=a,

y =b

n=7

and k= 4 since we have to find 5th term but k starts from zero

putting the values

`={7\choose 4}a^4b^(7-4)\\={7\choose 4}a^4b^(3)\\=(7!)/(4!(7-4)!)a^4b^3\\=35a^4b^3`

So, 5th term is 35a^4b^3