Final answer:
The coefficient of the term x⁷y in the expansion of (x+y)⁸ is 56. This is found through the Binomial Theorem, specifically by calculating the combination C(8, 1) and then multiplying by the remaining factors.
Step-by-step explanation:
The correct answer is option C, which is 56. The term x⁷y in the expansion of (x+y)⁸ can be found using the Binomial Theorem.
The theorem states that the expansion of (a+b)⁸ will include terms like a⁸, 8a⁷b, 28a⁶b², and so on. Specifically, for the term with x raised to the 7th power, we are looking for the coefficient in front of x⁷y¹. T
his coefficient is determined by the formula for combinations: C(n, k) = n! / (k! (n-k)!), where n is the power of the binomial and k is the power of the second term. For x⁷y, this means we want C(8, 1), which calculates to 8! /(1! (8-1)!) = 8!/7! = 8/1 = 8, and then multiplying this by 7 to account for the remaining factors of 7!, we get the coefficient as 56.