Fill in the blanks,(a) Number of terms in expansion `(-2x + 3y)^17` is _______.

Answer

To find the number of terms in the expansion of \((-2x + 3y)^{17}\), we can use the formula for the number of terms in the expansion of \((a + b)^n\), which is given by \(n + 1\).

### Step-by-Step Solution:

1. **Identify the values**: In the expression \((-2x + 3y)^{17}\), we can identify \(a = -2x\) and \(b = 3y\), and the exponent \(n = 17\).

2. **Apply the formula**: The formula for the number of terms in the expansion of \((a + b)^n\) is \(n + 1\).

3. **Calculate the number of terms**:
\[ \text{Number of terms} = n + 1 = 17 + 1 = 18 \]

4. **Final answer**: Therefore, the number of terms in the expansion of \((-2x + 3y)^{17}\) is **18**.