state true or false Common factor of `x^2y` and – `xy^(2)` is xy.

Answer

To determine whether the statement "the common factor of \( x^2y \) and \( -xy^2 \) is \( xy \)" is true or false, we can follow these steps:

### Step 1: Factor the expressions
We start by factoring both expressions.

1. The expression \( x^2y \) can be factored as:
\[ x^2y = x \cdot x \cdot y \]

2. The expression \( -xy^2 \) can be factored as:
\[ -xy^2 = -x \cdot y \cdot y \]

### Step 2: Identify common factors
Now, we will identify the common factors in both expressions.

- From \( x^2y \), we have the factors \( x, x, y \).
- From \( -xy^2 \), we have the factors \( -x, y, y \).

### Step 3: Compare the factors
Next, we compare the factors:

- The factor \( x \) is common in both expressions (only one \( x \) from \( -xy^2 \)).
- The factor \( y \) is also common (only one \( y \) from \( x^2y \)).

### Step 4: Write the common factor
The common factor that we can take from both expressions is:
\[ xy \]

### Conclusion
Since we have established that the common factor of \( x^2y \) and \( -xy^2 \) is indeed \( xy \), we can conclude that the statement is **true**.