Find the coefficient of the 3rd term in the expansion of (3𝑥 + 2𝑦)4a. 486b. 325c. 216d. None
Question
Solution
The expansion of (3x + 2y)^4 using the binomial theorem is:
(4C0)(3x)^4(2y)^0 + (4C1)(3x)^3(2y)^1 + (4C2)(3x)^2(2y)^2 + (4C3)(3x)^1(2y)^3 + (4C4)(3x)^0(2y)^4
The coefficient of the 3rd term is (4C2)(3x)^2(2y)^2.
4C2 = 4! / (2!(4-2)!) = 6
So, the coefficient of the 3rd term is 6*(3^2)(2^2) = 69*4 = 216.
So, the answer is c. 216.
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