Question

Find the constant term of (2x^3-1÷3x^2)^5​

Answer 1

Answer:

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Use the expansion (x + y)^n = sum_(k=0)^n C(n, k) x^(n - k)*y^k

The constant term for (3x^2 + 1/x)^9 is a term with no factors of x. This arrived at when x^(18 - 2k)/x^k = 1

=> 18 - 2k = k

=> 18 = 3k

=> k = 6

C(9, 6) = (9!)/((6!)*(3!)) = (9*8*7)/(3*2) = 84

The constant term is 3^3*84 = 2268