8 p square q square +9 pq square ;-6pq square -3 p square q square and -2 pq square +3 p square q square add the following

To solve this problem, we need to add the three given expressions:

1. \( 8p^2q^2 + 9pq^2 \)
2. \( -6pq^2 - 3p^2q^2 \)
3. \( -2pq^2 + 3p^2q^2 \)

Let's add these expressions step by step.

### Step 1: Combine like terms
- The like terms involving \( p^2q^2 \) are \( 8p^2q^2 \), \( -3p^2q^2 \), and \( 3p^2q^2 \).
- The like terms involving \( pq^2 \) are \( 9pq^2 \), \( -6pq^2 \), and \( -2pq^2 \).

### Step 2: Add the \( p^2q^2 \) terms
\[
8p^2q^2 - 3p^2q^2 + 3p^2q^2 = 8p^2q^2
\]

### Step 3: Add the \( pq^2 \) terms
\[
9pq^2 - 6pq^2 - 2pq^2 = 1pq^2
\]

### Final Answer
The sum of the expressions is:
\[
8p^2q^2 + pq^2
\]

This is the simplified result.

Would you like more details on how I arrived at this solution, or do you have any questions?

Here are five related questions you might find helpful:
1. How do you simplify expressions involving multiple terms with different variables?
2. What are the common techniques for factoring polynomial expressions?
3. How do you determine like terms in an algebraic expression?
4. How can you use the distributive property to combine like terms?
5. What are some methods to solve quadratic equations involving multiple variables?

**Tip:** Always double-check your work when combining like terms to avoid simple arithmetic errors.

Learn how to add polynomial expressions involving multiple terms with variables p and q. Follow a step-by-step solution to simplify the expression 8p^2q^2 + 9pq^2 - 6pq^2 - 3p^2q^2 - 2pq^2 + 3p^2q^2. Suitable for Grades 7-9.

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