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.
∑ ( ) 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.
