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The problem asks to factor the expression \( 13w^3 + 12w^2 \).

### Step-by-step solution:
1. **Identify the common factor**: Both terms have a common factor of \( w^2 \). So, we can factor out \( w^2 \) from the expression.
   
2. **Factor the expression**:
   \[
   13w^3 + 12w^2 = w^2(13w + 12)
   \]

Thus, the factored form of \( 13w^3 + 12w^2 \) is:
\[
w^2(13w + 12)
\]

Would you like a detailed explanation of any part of the factoring process? 

Here are five related questions:
1. How do you factor higher degree polynomials?
2. What happens if there is no common factor in the terms?
3. How do you handle factoring when variables have different exponents?
4. What is the difference between factoring and simplifying an expression?
5. Can you factor expressions with more than two terms?

**Tip**: Always check for the greatest common factor (GCF) first when factoring any expression.

Learn how to factor the polynomial expression 13w^3 + 12w^2 by identifying the greatest common factor (GCF) and applying the distributive property. This problem demonstrates key algebraic concepts, suitable for students in Grades 7-10.

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