Find the number of terms in the expansion of
`(3p+4q)^(14)`

Answer

To find the number of terms in the expansion of \((3p + 4q)^{14}\), we can use the formula for the number of terms in the binomial expansion.

### Step-by-Step Solution:

1. **Identify the Variables**:
In the expression \((3p + 4q)^{14}\), we have two terms: \(3p\) and \(4q\). Therefore, we can identify:
- \(r = 2\) (the number of different terms in the binomial)
- \(n = 14\) (the exponent)

2. **Use the Formula for Number of Terms**:
The formula to find the number of terms in the expansion of \((a + b)^n\) is given by:
\[ \text{Number of terms} = n + r - 1 \]
where \(n\) is the exponent and \(r\) is the number of different terms.

3. **Substitute the Values**:
Now, substituting the values of \(n\) and \(r\) into the formula:
\[ \text{Number of terms} = 14 + 2 - 1 \]

4. **Calculate**:
Simplifying the expression:
\[ \text{Number of terms} = 14 + 2 - 1 = 15 \]

5. **Conclusion**:
Therefore, the number of terms in the expansion of \((3p + 4q)^{14}\) is **15**.