Question

What is the coefficient of x²y^8 in the expansion of (x + y)^10?

Answer 1

Answer: 45

Explanation:

We know that
`(m+1)^(th)` term in the binomial expansion of
`(a+b)^n` is given by :-

`T_(r+1)=^nC_m a^(n-m)b^m`

Now,
`(m+1)^(th)` term for the binomial expansion of
`(x+y)^(10)` is given by :-

`T_(r+1)=^(10)C_m x^(10-m)y^m` (1)

When we compare (1) to
`x^2y^8` , we get m=8

Then, the coefficient of
`x^2y^8` from (1) will be :-

`^(10)C_8=(10!)/(8!(10-8)!)\\\\=(10*9*8!)/(8!2!)=45`

Hence, the coefficient of
`x^2y^8` is 45.