Question

What is the coeffieent of (x^4)(y^4) in the expansion of (x+y)^8

Answer 1

ANSWER

The coefficient is 70.

Step-by-step explanation

The given binomial expression is


`(x+y)^8`

The specific term of a binomial expansion can be determined using the formula,


`T_(r+1)= nC_ra^(n-r)b^r`
where


`n=8,r=4,a=x,b=y`

We substitute these values into the formula to get,


`T_(4+1)= 8C_4x^(8-4)y^4`

We simplify to get,


`T_(5)= 70x^(4)y^4`

Hence the coefficient is 70.