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Find the term independent of x, where x ...

Find the term independent of `x`, where `x != 0`, in the expansion of `((3x^(2))/(2) - (1)/(3x))^(15)`.

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To find the term independent of \( x \) in the expansion of \( \left( \frac{3x^2}{2} - \frac{1}{3x} \right)^{15} \), we will follow these steps: ### Step 1: Identify the General Term The general term \( T_{r+1} \) in the binomial expansion of \( (a + b)^n \) is given by: \[ T_{r+1} = \binom{n}{r} a^{n-r} b^r \] In our case, \( a = \frac{3x^2}{2} \) and \( b = -\frac{1}{3x} \), and \( n = 15 \). Thus, the general term becomes: ...
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