Which of the following are like terms?

Options

A. `5xyz ^(2) , - 3 xy^(3)z`
B. `- 5 xyz ^(2) , 7 xyz ^(2)`
C. `5 xyz ^(2), 5x ^(2) yz`
D. `5 xyz ^(3), x ^(2) y ^(2) z ^(2)`

Answer

To determine which of the following are like terms, we need to follow these steps:

### Step 1: Identify the Terms
List out the terms given in the question. For example, let's say we have the following terms:
1. \( 3xy^2 \)
2. \( 5xy^2 \)
3. \( 2xyz \)
4. \( 4x^2y \)

### Step 2: Check the Variables
Look at the variables in each term. Like terms must have the same variables raised to the same powers.

- For \( 3xy^2 \): Variables are \( x \) and \( y^2 \).
- For \( 5xy^2 \): Variables are \( x \) and \( y^2 \).
- For \( 2xyz \): Variables are \( x \), \( y \), and \( z \).
- For \( 4x^2y \): Variables are \( x^2 \) and \( y \).

### Step 3: Compare the Terms
Now, compare the terms based on their variables and powers:
- \( 3xy^2 \) and \( 5xy^2 \) are like terms because they have the same variables \( x \) and \( y^2 \).
- \( 2xyz \) is not a like term with \( 3xy^2 \) or \( 5xy^2 \) because it includes \( z \).
- \( 4x^2y \) is also not a like term with \( 3xy^2 \) or \( 5xy^2 \) because the power of \( x \) is different.

### Conclusion
The like terms among the given options are \( 3xy^2 \) and \( 5xy^2 \).

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