Which of the following is a pair of like terms?

Options

A. `-7xy^2z, - 7x^2yz`
B. `- 10xyz^2, 3xyz^2`
C. `3xyz, 3x^2y^2z^2`
D. `4xyz^2, 4x^2yz`

Answer

To determine which of the following is a pair of like terms, we first need to understand what like terms are. Like terms are terms that contain the same variable(s) raised to the same power(s).

Let's analyze each option step by step:

1. **Identify the Terms**:
- Option 1: \(-7xy^2z\) and \(-7x^2yz\)
- Option 2: \(-10xyz^2\) and \(3xyz^2\)
- Option 3: \(3xyz\) and \(3x^2y^2z^2\)
- Option 4: \(4xyz^2\) and \(4x^2yz\)

2. **Check Option 1**:
- Terms: \(-7xy^2z\) and \(-7x^2yz\)
- Variables:
- First term: \(x^1, y^2, z^1\)
- Second term: \(x^2, y^1, z^1\)
- Since the powers of \(x\) and \(y\) are different, these are **not like terms**.

3. **Check Option 2**:
- Terms: \(-10xyz^2\) and \(3xyz^2\)
- Variables:
- Both terms have \(x^1, y^1, z^2\)
- Since both terms have the same variables raised to the same powers, these are **like terms**.

4. **Check Option 3**:
- Terms: \(3xyz\) and \(3x^2y^2z^2\)
- Variables:
- First term: \(x^1, y^1, z^1\)
- Second term: \(x^2, y^2, z^2\)
- The powers of \(x\) and \(y\) are different, so these are **not like terms**.

5. **Check Option 4**:
- Terms: \(4xyz^2\) and \(4x^2yz\)
- Variables:
- First term: \(x^1, y^1, z^2\)
- Second term: \(x^2, y^1, z^1\)
- The powers of \(x\) are different, so these are **not like terms**.

**Conclusion**: The only pair of like terms is found in **Option 2**: \(-10xyz^2\) and \(3xyz^2\).