Find the number of terms in the expansion of `(2/p +p/2)^8`

Answer

To find the number of terms in the expansion of \((\frac{2}{p} + \frac{p}{2})^8\), we can follow these steps:

### Step 1: Identify the components of the binomial expression
We can rewrite the expression in the form of \( (x + y)^n \), where:
- \( x = \frac{2}{p} \)
- \( y = \frac{p}{2} \)
- \( n = 8 \)

### Step 2: Use the formula for the number of terms in a binomial expansion
The number of terms in the expansion of \( (x + y)^n \) is given by the formula:
\[ \text{Number of terms} = n + 1 \]

### Step 3: Substitute the value of \( n \)
In our case, \( n = 8 \). Therefore, we can calculate the number of terms as follows:
\[ \text{Number of terms} = 8 + 1 = 9 \]

### Conclusion
Thus, the number of terms in the expansion of \((\frac{2}{p} + \frac{p}{2})^8\) is \( 9 \).

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