Classify into monomials, binomials and trinomials.
`3x^2+xy-4yx`

Answer

To classify the expression \(3x^2 + xy - 4yx\) into monomials, binomials, or trinomials, we can follow these steps:

### Step 1: Identify the Terms
The expression given is \(3x^2 + xy - 4yx\). We need to identify how many distinct terms are present in this expression.

### Step 2: Count the Terms
1. The first term is \(3x^2\).
2. The second term is \(xy\).
3. The third term is \(-4yx\).

### Step 3: Combine Like Terms (if necessary)
Notice that \(xy\) and \(-4yx\) are actually like terms because \(yx\) is the same as \(xy\). Therefore, we can combine them:
- The expression can be rewritten as:
\[ 3x^2 + xy - 4xy = 3x^2 - 3xy \]

### Step 4: Count the Distinct Terms Again
Now, we have:
1. \(3x^2\)
2. \(-3xy\)

This gives us a total of **2 distinct terms**.

### Step 5: Classify the Expression
Since there are 2 terms in the expression, we classify it as a **binomial**.

### Final Answer
The expression \(3x^2 + xy - 4yx\) is classified as a **binomial**.

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