The coefficient of xy in `3x^2 zy + 7 xyz - 2z^2x` is

Options

A. 3z
B. `-2`
C. 7xy
D. 7z

Answer

To find the coefficient of \( xy \) in the expression \( 3x^2zy + 7xyz - 2z^2x \), we will analyze each term in the expression step by step.

### Step 1: Identify the terms in the expression
The given expression is:
\[ 3x^2zy + 7xyz - 2z^2x \]

### Step 2: Break down each term
1. **First term:** \( 3x^2zy \)
- This term contains \( xy \) but is multiplied by \( x \) (specifically \( x^2 \)), so it does not contribute to the coefficient of \( xy \).

2. **Second term:** \( 7xyz \)
- This term contains \( xy \) along with \( z \). We can factor it as:
\[ 7xyz = 7z \cdot xy \]
- Here, the coefficient of \( xy \) is \( 7z \).

3. **Third term:** \( -2z^2x \)
- This term does not contain \( y \), so it does not contribute to the coefficient of \( xy \).

### Step 3: Collect the coefficients
From our analysis:
- The only term that contributes to the coefficient of \( xy \) is \( 7xyz \), which gives us the coefficient \( 7z \).

### Final Answer
Thus, the coefficient of \( xy \) in the expression \( 3x^2zy + 7xyz - 2z^2x \) is:
\[ \boxed{7z} \]