Respuesta :

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.

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:

[tex] (x + y) ^ 8
[/tex]

Therefore, the value of n is given by:

[tex] n = 1
[/tex]

We have the following term:

[tex] Cx ^ 7y
[/tex]

Therefore, the value of k is given by:

[tex] k = 1
[/tex]

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

[tex] 8x ^ 7y
[/tex]

Thus,

[tex] C = 8
[/tex]

Answer:

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

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