In the following, which pair contains like terms ?

Options

A. `2x^(2),y 2xy^(2)`
B. `2xy-3yx`
C. `6,6x`
D. `2xy, 3xyz`

Answer

To determine which pair contains like terms, we need to identify pairs of algebraic expressions that have the same variables raised to the same powers. Let's analyze the given pairs step by step.

### Step 1: Identify the pairs of terms
The pairs of terms provided are:
1. \(2xy\) and \(-3yx\)
2. \(6\) and \(6x\)
3. \(2xy\) and \(3xyz\)

### Step 2: Analyze the first pair \(2xy\) and \(-3yx\)
- Both terms have the same variables: \(x\) and \(y\).
- The order of the variables does not matter in multiplication (i.e., \(xy\) is the same as \(yx\)).
- Therefore, \(2xy\) and \(-3yx\) are like terms.

### Step 3: Analyze the second pair \(6\) and \(6x\)
- The first term \(6\) is a constant, while the second term \(6x\) contains the variable \(x\).
- Since one term is a constant and the other contains a variable, they are not like terms.

### Step 4: Analyze the third pair \(2xy\) and \(3xyz\)
- The first term \(2xy\) contains the variables \(x\) and \(y\), while the second term \(3xyz\) contains \(x\), \(y\), and an additional variable \(z\).
- Because the presence of the variable \(z\) in the second term makes it different from the first term, they are not like terms.

### Conclusion
From the analysis, the only pair that contains like terms is:
- \(2xy\) and \(-3yx\)

Thus, the answer is the first pair.

### Final Answer
The pair that contains like terms is \(2xy\) and \(-3yx\).

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