Find the middle term inn
(i) `((2y^(2))/(3)+(3)/(2y^(2)))^(9),y ne0`
(ii) `(4x^(2)+9y^(2)+12xy)^(n)`

Explanation

To find the middle term in the given expressions, we will follow the Binomial Theorem and the concept of middle terms in binomial expansions.

### (i) Find the middle term in \(\left(\frac{2y^2}{3} + \frac{3}{2y^2}\right)^9\)

1. **Identify the total number of terms**: The number of terms in the expansion of \((a + b)^n\) is \(n + 1\). Here, \(n = 9\), so the number of terms is \(9 + 1 = 10\), which is even.

2. **Determine the middle terms**: For an even \(n\), the middle terms are \(T_{\frac{n}{2}} = T_5\) and \(T_{\frac{n}{2} + 1} = T_6\).

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