https://file.aiquickdraw.com/mathbot/file/1726603614607w0nmqkn8.jpg

The expression in the image is:

\[
2a^3 - 4a^2 + 8a
\]

Let's simplify this expression by factoring it.

### Step 1: Factor out the greatest common factor (GCF)

The terms are \(2a^3\), \(-4a^2\), and \(8a\). The GCF of these terms is \(2a\).

So, factor out \(2a\):

\[
2a(a^2 - 2a + 4)
\]

### Final Answer:
\[
2a(a^2 - 2a + 4)
\]

Let me know if you have any questions or if you'd like to go into more details!

### Follow-up Questions:
1. How do we determine the greatest common factor for polynomial expressions?
2. Can the quadratic \(a^2 - 2a + 4\) be factored further?
3. What is the importance of factoring in solving equations?
4. How would this expression change if \(a = 2\)?
5. What would happen if there were more terms in the original expression?

### Tip:
Always check for common factors in all terms before attempting more complex factorization methods.

Learn how to factor the polynomial expression 2a^3 - 4a^2 + 8a by extracting the greatest common factor (GCF). This problem covers key algebraic concepts and methods related to polynomial factorization. Suitable for students in Grades 8-10.

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