Which is the like term as `24 a^(2) bc ` ?

Options

A. `13 xx 8a xx 2b xx c xx a `
B. `8 xx 3 xx a xx b xx c`
C. `3 xx 8xx a xx b xx c xx c`
D. `8 xx 8 xx a xx b xx c`

Answer

To determine which term is a like term to \( 24a^2bc \), we need to identify terms that have the same variable components. Like terms are those that have identical variable parts, regardless of their coefficients.

### Step-by-Step Solution:

1. **Identify the given term**: The term we are comparing to is \( 24a^2bc \). Here, the variable part is \( a^2bc \).

2. **Understand what like terms are**: Like terms must have the same variables raised to the same powers. In this case, we need to find a term that has \( a^2 \), \( b \), and \( c \) in it.

3. **Analyze the options**: We need to check each option to see if it has the same variable part \( a^2bc \).

- **Option 1**: \( 13 \times 8a \times 2b \times c \times a \)
- This can be simplified to \( 13 \times 8 \times 2 \times a^2 \times b \times c = 208a^2bc \).
- This is a like term because it has \( a^2bc \).

- **Option 2**: \( 8 \times 3 \times a \times b \times c \)
- This simplifies to \( 24abc \).
- This is not a like term because it has \( abc \) instead of \( a^2bc \).

- **Option 3**: \( 3 \times 8 \times a \times b \times c^2 \)
- This simplifies to \( 24abc^2 \).
- This is not a like term because it has \( abc^2 \) instead of \( a^2bc \).

- **Option 4**: \( 4 \times 8 \times a \times b \times c \)
- This simplifies to \( 32abc \).
- This is not a like term because it has \( abc \) instead of \( a^2bc \).

4. **Conclusion**: The only option that is a like term to \( 24a^2bc \) is **Option 1**.

### Final Answer:
The like term as \( 24a^2bc \) is **Option 1**.