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

Answer:

$5m^4 n$

Step-by-step 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 = $^5C_1 m^{5-1} n^1$

$=\frac{5!}{1!4!} m^4 n^1$

$=5m^4 n$