Subtract `4p^(2)q+pq^(2)-3pq+7q-8p-10` from `5p^(2)q-2pq^(2)+5pq-11q-3p+28`.

Answer

To solve the problem of subtracting \(4p^2q + pq^2 - 3pq + 7q - 8p - 10\) from \(5p^2q - 2pq^2 + 5pq - 11q - 3p + 28\), we will follow these steps:

### Step 1: Write down the expressions
We have two expressions:
1. \(5p^2q - 2pq^2 + 5pq - 11q - 3p + 28\)
2. \(4p^2q + pq^2 - 3pq + 7q - 8p - 10\)

We need to subtract the second expression from the first.

### Step 2: Rewrite the subtraction
To subtract the second expression from the first, we can rewrite it as:
\[ (5p^2q - 2pq^2 + 5pq - 11q - 3p + 28) - (4p^2q + pq^2 - 3pq + 7q - 8p - 10) \]

### Step 3: Distribute the negative sign
We will distribute the negative sign across the second expression:
\[ 5p^2q - 2pq^2 + 5pq - 11q - 3p + 28 - 4p^2q - pq^2 + 3pq - 7q + 8p + 10 \]

### Step 4: Combine like terms
Now we will combine the like terms:

1. For \(p^2q\):
\[ 5p^2q - 4p^2q = 1p^2q \]

2. For \(pq^2\):
\[ -2pq^2 - pq^2 = -3pq^2 \]

3. For \(pq\):
\[ 5pq + 3pq = 8pq \]

4. For \(q\):
\[ -11q - 7q = -18q \]

5. For \(p\):
\[ -3p + 8p = 5p \]

6. For the constant:
\[ 28 + 10 = 38 \]

### Step 5: Write the final expression
Combining all the results, we get:
\[ p^2q - 3pq^2 + 8pq - 18q + 5p + 38 \]

### Final Answer:
\[ p^2q - 3pq^2 + 8pq - 18q + 5p + 38 \]

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