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:
\((x + y) ^ 8
\)
Therefore, the value of n is given by:
\(n = 1
\)
We have the following term:
\(Cx ^ 7y
\)
Therefore, the value of k is given by:
\(k = 1
\)
Substituting values and calculating (see attached image), we have that the value of the coefficient is given by:
\(8x ^ 7y
\)
Thus,
\(C = 8
\)
Answer:
The value of the coefficient for the term x^7y is 8.
