Question

What is the second term of (m+n)^5

Answer 1

the second term of (m+n)^5 will be 5m^4n

Answer 2

`5m^4 n`

Explanation:

By the binomial expansion,

`(a+b)^n =\sum_(r=0)^(n) ^nC_r a^(n-r) b^r`

Using this,

`(m+n)^5 =\sum_(r=0)^(5) ^5C_r m^(5-r) n^r`

For finding 2nd term,

Put r = 1, ( because terms start from 0 to 5 )

Second term =
`^5C_1 m^(5-1) n^1`

`=(5!)/(1!4!) m^4 n^1`

`=5m^4 n`