Which of the following are like terms?

Options

A. `-5xy,5x`
B. `-5xy, 3yz`
C. `-5xy, -5y`
D. `-5xy, 7xy`

Answer

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

### Step 1: Understand Like Terms
Like terms are terms that have the same variable(s) raised to the same power(s). The coefficients (numbers in front of the variables) can be different, but the variables and their exponents must be identical.

### Step 2: Identify the Terms
Let's say we have the following terms to analyze:
1. -5xy
2. 5x
3. -5xy
4. 7xy

### Step 3: Compare Each Pair of Terms
- **Comparing -5xy and 5x**:
- The first term is -5xy (which has variables x and y).
- The second term is 5x (which has only variable x).
- Since the variables are not the same (one has y and the other does not), these are **not like terms**.

- **Comparing -5xy and -5xy**:
- Both terms are identical (-5xy).
- Since both terms have the same variable part and exponent part, these are **like terms**.

- **Comparing -5xy and 7xy**:
- Both terms have the same variable part (xy).
- Since both terms have the same variable part and exponent part, these are **like terms**.

- **Comparing 5x and 7xy**:
- The first term is 5x (which has only variable x).
- The second term is 7xy (which has variables x and y).
- Since the variables are not the same (one has y and the other does not), these are **not like terms**.

### Conclusion
The like terms from the given options are:
- -5xy and 7xy
- -5xy and -5xy

### Final Answer
The like terms are: **-5xy and 7xy, -5xy and -5xy.**

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