The problem asks to factor out the greatest common factor (GCF) from the expression $2a^2b^3 - 18a^3b^3 + 2a^3b^2 - 8a^4b^2$.

1. Problem Description

The problem asks to factor out the greatest common factor (GCF) from the expression $2a^2b^3 - 18a^3b^3 + 2a^3b^2 - 8a^4b^2$.

2. Solution Steps

First, we identify the greatest common factor of the coefficients: 2, -18, 2, and -

8. The GCF is

2. Next, we identify the greatest common factor of the powers of $a$: $a^2$, $a^3$, $a^3$, and $a^4$. The GCF is $a^2$.

Then, we identify the greatest common factor of the powers of $b$: $b^3$, $b^3$, $b^2$, and $b^2$. The GCF is $b^2$.

Therefore, the GCF of the entire expression is $2a^2b^2$.

Now, we factor out $2a^2b^2$ from each term in the expression:

$2a^2b^3 = 2a^2b^2(b)$

$-18a^3b^3 = 2a^2b^2(-9ab)$

$2a^3b^2 = 2a^2b^2(a)$

$-8a^4b^2 = 2a^2b^2(-4a^2)$

Putting it all together, we have:

$2a^2b^3 - 18a^3b^3 + 2a^3b^2 - 8a^4b^2 = 2a^2b^2(b - 9ab + a - 4a^2)$

3. Final Answer

$2a^2b^2(b - 9ab + a - 4a^2)$