What should be subtracted from `2p^2+3q^2 +6pq` to get `p^2-q^2` ?

Answer

To solve the problem of what should be subtracted from \(2p^2 + 3q^2 + 6pq\) to get \(p^2 - q^2\), we can follow these steps:

### Step 1: Set up the equation
We need to find \(x\) such that:
\[ 2p^2 + 3q^2 + 6pq - x = p^2 - q^2 \]

### Step 2: Rearrange the equation
To find \(x\), we can rearrange the equation:
\[ x = 2p^2 + 3q^2 + 6pq - (p^2 - q^2) \]

### Step 3: Distribute the negative sign
Now, distribute the negative sign across the terms in the parentheses:
\[ x = 2p^2 + 3q^2 + 6pq - p^2 + q^2 \]

### Step 4: Combine like terms
Now, combine the like terms:
- For \(p^2\): \(2p^2 - p^2 = 1p^2\)
- For \(q^2\): \(3q^2 + q^2 = 4q^2\)
- The \(6pq\) term remains as is.

So, we have:
\[ x = p^2 + 4q^2 + 6pq \]

### Final Answer
Thus, the expression that should be subtracted is:
\[ \boxed{p^2 + 4q^2 + 6pq} \]

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