To factor the expression \( 2a - 6ab^2 + 4a^2b \), we can follow these steps:

### Step 1: Identify the greatest common factor (GCF)
First, let's identify the greatest common factor (GCF) of all the terms:

- The GCF of the coefficients \(2\), \(-6\), and \(4\) is \(2\).
- The GCF of the variable parts is \(a\) since \(a\) is present in all terms.

Thus, the GCF of the entire expression is \(2a\).

### Step 2: Factor out the GCF
Now, factor out \(2a\) from each term:

\[
2a - 6ab^2 + 4a^2b = 2a(1 - 3b^2 + 2ab)
\]

### Final Factored Form
The factored form of the expression is:

\[
2a(1 - 3b^2 + 2ab)
\]

Would you like more details on any step, or do you have any questions?

### Related Questions:
1. How do you find the greatest common factor of an algebraic expression?
2. Can you explain how to factor polynomials by grouping?
3. What is the difference between factoring and expanding an expression?
4. How do you factor a quadratic expression?
5. Can you factor the expression \(6x^2 - 15xy + 9x\)?

### Tip:
Always check each term for common factors, including both coefficients and variable parts, to ensure you factor out the greatest common factor.

Learn how to factor the algebraic expression 2a - 6ab^2 + 4a^2b with detailed steps. This problem involves factoring by identifying the greatest common factor (GCF) and applying it to each term. Suitable for high school students studying algebra.

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