How many terms are there in `3x-(4)/(5)xy^(2)-(1)/(5)xy^(2)-(2)/(3)y`?

Answer

To determine how many terms are in the expression \(3x - \frac{4}{5}xy^2 - \frac{1}{5}xy^2 - \frac{2}{3}y\), we will analyze the expression step by step.

### Step-by-Step Solution:

1. **Identify the Expression**: The given expression is \(3x - \frac{4}{5}xy^2 - \frac{1}{5}xy^2 - \frac{2}{3}y\).

2. **Recognize the Terms**: In algebraic expressions, terms are separated by the addition (+) or subtraction (−) signs.

3. **List the Terms**:
- The first term is \(3x\).
- The second term is \(-\frac{4}{5}xy^2\).
- The third term is \(-\frac{1}{5}xy^2\).
- The fourth term is \(-\frac{2}{3}y\).

4. **Count the Terms**: Now, we count the distinct parts we identified:
- \(3x\) (1st term)
- \(-\frac{4}{5}xy^2\) (2nd term)
- \(-\frac{1}{5}xy^2\) (3rd term)
- \(-\frac{2}{3}y\) (4th term)

5. **Final Count**: There are a total of 4 terms in the expression.

### Conclusion:
The number of terms in the expression \(3x - \frac{4}{5}xy^2 - \frac{1}{5}xy^2 - \frac{2}{3}y\) is **4**.

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