Let's simplify the expression: 

Given:
\[ 10w + 3w^2 - 6w - 6w + 9w \]

### Step 1: Combine like terms
Group the terms with \( w^2 \) and \( w \):
\[ 3w^2 + (10w - 6w - 6w + 9w) \]

### Step 2: Simplify the \( w \) terms
\[ 10w - 6w - 6w + 9w = 7w \]

### Step 3: Write the simplified expression
\[ 3w^2 + 7w \]

### Final Answer:
The simplified expression is:
\[ 3w^2 + 7w \]

Would you like more details or have any questions on how the simplification was done?

Here are some related questions:
1. How do you factor the expression \(3w^2 + 7w\)?
2. What are the coefficients in the expression \(3w^2 + 7w\)?
3. How do you solve the equation if \(3w^2 + 7w = 0\)?
4. What are like terms in algebra, and how are they combined?
5. How does distributing work when simplifying expressions?

**Tip:** Always group and combine like terms systematically to avoid errors during simplification.

Simplify the polynomial expression 10w + 3w^2 - 6w - 6w + 9w by combining like terms. This solution involves key algebraic concepts such as combining like terms and polynomial properties. Suitable for students in Grades 7-9.

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