Subtract:
`4pq - 5a^(2) - 3p^(2) "from" 5p^(2) + 3q^(2) - pq`

Answer

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

### Step 1: Write the expression for subtraction
We need to subtract \( 4pq - 5a^2 - 3p^2 \) from \( 5p^2 + 3q^2 - pq \). This can be written as:
\[ (5p^2 + 3q^2 - pq) - (4pq - 5a^2 - 3p^2) \]

### Step 2: Distribute the negative sign
Distributing the negative sign across the second expression gives:
\[ 5p^2 + 3q^2 - pq - 4pq + 5a^2 + 3p^2 \]

### Step 3: Combine like terms
Now, we will combine the like terms:
- Combine \( 5p^2 \) and \( 3p^2 \):
\[ 5p^2 + 3p^2 = 8p^2 \]
- Combine \( -pq \) and \( -4pq \):
\[ -pq - 4pq = -5pq \]
- The \( 3q^2 \) and \( 5a^2 \) terms remain as they are since there are no like terms to combine with them.

### Step 4: Write the final expression
Putting it all together, we get:
\[ 8p^2 + 3q^2 + 5a^2 - 5pq \]

### Final Answer
Thus, the result of subtracting \( 4pq - 5a^2 - 3p^2 \) from \( 5p^2 + 3q^2 - pq \) is:
\[ 8p^2 + 3q^2 + 5a^2 - 5pq \]

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