The given expression is \( 15n^3 + 12n \). To simplify it, we can factor out the greatest common factor (GCF).

### Step 1: Find the GCF of the terms
- The terms are \( 15n^3 \) and \( 12n \).
- The GCF of the coefficients 15 and 12 is 3.
- The lowest power of \( n \) that appears in both terms is \( n \).

So, the GCF is \( 3n \).

### Step 2: Factor out the GCF
Now, factor \( 3n \) out of the expression:

\[
15n^3 + 12n = 3n(5n^2 + 4)
\]

### Simplified Expression
\[
\boxed{3n(5n^2 + 4)}
\]

Would you like more details, or do you have any questions? Here are some related problems you might find useful:

1. How do you factor \( 18n^4 + 24n^2 \)?
2. What is the GCF of \( 20n^3 + 35n \)?
3. How do you factorize polynomials with higher powers, like \( n^4 \)?
4. How do you factor trinomials like \( 6n^2 + 11n + 3 \)?
5. What are the steps to simplify expressions with more than two terms?

**Tip:** Always look for the GCF first when simplifying polynomial expressions; it can make the factoring process much easier!

Simplify the polynomial 15n^3 + 12n by factoring out the greatest common factor (GCF). Learn how to factor this expression with a step-by-step explanation and understand the process of finding the GCF. Suitable for students in Grades 7-9.

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