The like terms in `3x(3-2y) and 2(xy+x^2)` are

Options

A. `9x and 2x^2`
B. `-6xy and 2xy`
C. `9x and 2xy`
D. `-6xy and 2x^2`

Answer

To find the like terms in the expressions \(3x(3 - 2y)\) and \(2(xy + x^2)\), we will simplify both expressions and identify the like terms.

### Step-by-Step Solution:

1. **Expand the first expression \(3x(3 - 2y)\)**:
- Distribute \(3x\) to both terms inside the parentheses.
- Calculation:
\[ 3x \cdot 3 - 3x \cdot 2y = 9x - 6xy \]
- So, the first expression simplifies to \(9x - 6xy\).

2. **Expand the second expression \(2(xy + x^2)\)**:
- Distribute \(2\) to both terms inside the parentheses.
- Calculation:
\[ 2 \cdot xy + 2 \cdot x^2 = 2xy + 2x^2 \]
- So, the second expression simplifies to \(2xy + 2x^2\).

3. **Identify like terms**:
- Now we have:
- From the first expression: \(9x - 6xy\)
- From the second expression: \(2xy + 2x^2\)
- The like terms are those that have the same variables raised to the same powers.
- Here, the like terms are:
- The \(xy\) terms: \(-6xy\) from the first expression and \(2xy\) from the second expression.

4. **Final answer**:
- The like terms in the given expressions are \(-6xy\) and \(2xy\).