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Answer :
Final answer:
The coefficient of x⁴y⁴ in the expansion of (x + y)⁸ is determined using the binomial theorem. It is found by calculating the binomial coefficient C(8, 4), which is 70.
Explanation:
The coefficient of x⁴y⁴ in the expansion of (x + y)⁸ can be determined using the binomial theorem. The general term in the expansion of (a + b)⁸ is given by t(n,k) = C(n, k) · a⁸−k · b⁴, where C(n, k) is the binomial coefficient for the nth term and kth position, calculated as C(n, k) = n! / [k! · (n-k)!]. For the x⁴y⁴ term, k will be 4, thus the binomial coefficient will be C(8, 4) = 8! / [4! · (8-4)!] = 70. Therefore, the coefficient of x⁴y⁴ is 70.
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