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:

$(x + y) ^ 8$

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.