Classify into monomials, binomials and trinomials.
`p^2+q^2+r^2-4q^2`

Answer

To classify the expression \( p^2 + q^2 + r^2 - 4q^2 \) into monomials, binomials, and trinomials, follow these steps:

### Step 1: Identify the Expression
The given expression is:
\[ p^2 + q^2 + r^2 - 4q^2 \]

### Step 2: Combine Like Terms
We need to simplify the expression by combining like terms. The terms \( q^2 \) and \( -4q^2 \) are like terms.

\[ q^2 - 4q^2 = -3q^2 \]

Now, substitute this back into the expression:
\[ p^2 - 3q^2 + r^2 \]

### Step 3: Count the Terms
Now, let's count the number of distinct terms in the simplified expression:
1. \( p^2 \)
2. \( -3q^2 \)
3. \( r^2 \)

There are three terms in total.

### Step 4: Classify the Expression
Since the expression has three terms, it is classified as a **trinomial**.

### Final Answer
The expression \( p^2 + q^2 + r^2 - 4q^2 \) simplifies to \( p^2 - 3q^2 + r^2 \) and is classified as a **trinomial**.

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