simplify (4pq + 2p2q − 9pq2) − (3p2q − 4pq + 12pq2)

Let's simplify the expression \((4pq + 2p^2q − 9pq^2) − (3p^2q − 4pq + 12pq^2)\).

1. **Distribute the negative sign across the second group:**
   \[
   4pq + 2p^2q − 9pq^2 − 3p^2q + 4pq − 12pq^2
   \]

2. **Group like terms:**
   \[
   (4pq + 4pq) + (2p^2q − 3p^2q) + (−9pq^2 − 12pq^2)
   \]

3. **Simplify each group:**
   - \(4pq + 4pq = 8pq\)
   - \(2p^2q − 3p^2q = −p^2q\)
   - \(−9pq^2 − 12pq^2 = −21pq^2\)

4. **Combine the simplified terms:**
   \[
   8pq − p^2q − 21pq^2
   \]

So, the simplified expression is:

\[
8pq − p^2q − 21pq^2
\]

Would you like more details or have any questions?

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**Related Questions:**
1. How would you factor the expression \(8pq − p^2q − 21pq^2\)?
2. What happens if you change the signs in the original expression?
3. Can you express the simplified result in terms of a common factor?
4. How would you simplify \( (pq)(4 + 2p - 9q) - (pq)(3p - 4 + 12q) \)?
5. What if one of the variables equals 1 in the expression?

**Tip:** Always be careful with the distribution of negative signs when subtracting expressions. It changes the sign of every term inside the parentheses.

Learn how to simplify the algebraic expression 4pq + 2p^2q - 9pq^2 - (3p^2q - 4pq + 12pq^2) step-by-step. This problem involves combining like terms and distributing negative signs. Suitable for students in Grades 7-9.

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