The number of distinct terms in the expansion of `(x+1/x+x^2+1/(x^2))^(15)` is/are (with respect to different power of `x` ) `255` b. `61` c. `127` d. none of these

Options

A. 255
B. 61
C. 127
D. none of these

Explanation

To find the number of distinct terms in the expansion of \((x + \frac{1}{x} + x^2 + \frac{1}{x^2})^{15}\), we can follow these steps:

### Step 1: Simplify the Expression
We start with the expression:
\[ (x + \frac{1}{x} + x^2 + \frac{1}{x^2})^{15} \]
To simplify, we can combine the terms:
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