Question

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

Answer 1

Answer:  45

Step-by-step 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 :-

$^{10}C_8=\dfrac{10!}{8!(10-8)!}\\\\=\dfrac{10\times9\times8!}{8!2!}=45$

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