The problem asks us to factor out the greatest common factor from the expression $8a^2b^3 - 72ab + 16a$.

1. Problem Description

The problem asks us to factor out the greatest common factor from the expression $8a^2b^3 - 72ab + 16a$.

2. Solution Steps

We need to find the greatest common factor (GCF) of the terms $8a^2b^3$, $-72ab$, and $16a$.

First, consider the coefficients: 8, -72, and

1

6. The GCF of these numbers is 8 since $8 = 8 \times 1$, $72 = 8 \times 9$, and $16 = 8 \times 2$.

Next, consider the variable $a$. The terms are $a^2$, $a$, and $a$. The GCF is $a$.

Now, consider the variable $b$. The terms are $b^3$, $b$, and no $b$ in the last term. Therefore, $b$ is not part of the GCF.

Thus, the GCF of the three terms is $8a$.

Now, we factor out the GCF from each term:

$8a^2b^3 = (8a)(ab^3)$

$-72ab = (8a)(-9b)$

$16a = (8a)(2)$

Therefore, we can write the expression as:

$8a^2b^3 - 72ab + 16a = 8a(ab^3 - 9b + 2)$.

3. Final Answer

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