二項式定理

For the binomial expression ( a + b)^n, general term is nCr a^(n - r)b^r ( r = 0 to n).
Now a = x^2, b = 3/x and n = 9
So general term is 9Cr (x^2)^(9 - r) (3/x)^r
= 9Cr x^(18 - 2r)(3^r)[x^(-r)]
= 9Cr (3^r) x^(18 - 3r)
For the term x^9, that is 18 - 3r = 9, r = 3
So coefficient of the x^9 term is 9C3 ( 3^3) = 9C3 x 27 = 2268.

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題目應該是 [ x^2 + (3/x) ]^6 ?

(x^2)^(6-r) * [ x^(-1) ]^r = x^9

12 - 2r - r = 9
3 = 3r
r = 1

∴x^9的系數 = 6C1 * 3^1 = 18

https://www.wolframalpha.com/input/?i=(x%5E2%20%2B%203%2Fx%20)%5E9&t=crmtb01

答案是 2268