Question

What is the coefficient of the term x7y in the expansion of (x + y)8?

Answer 1

We have to find the coefficient of the term x^7 y in the expansion of:( x + y ) ^8a = x, b = y, n = 8And the expansion is: n n
∑ ( ) a ^(n-k) b ^k
k=0 ka^(n-k) b^k = x^7 ySo : k = 1nCk = 8C1 = 8Answer: The coefficient of the term x^7y is 8.

Answer 2

By definition we have that the binomial expansion theorem is given by:

(see attached image)

From here, we must replace the values of k and n correctly.

We have a binomial of the form:

`image`

Therefore, the value of n is given by:

`image`

We have the following term:

`image`

Therefore, the value of k is given by:

`image`

Substituting values and calculating (see attached image), we have that the value of the coefficient is given by:

`image`

Thus,

`image`

Answer:

The value of the coefficient for the term x^7y is 8.