Find the Equivalent Expression: Simplifying 99ab² + 81b

To solve this problem, we'll follow these steps:

• Step 1: Identify the greatest common factor (GCF) of the coefficients in the expression.

• Step 2: Factor out the GCF from the entire expression.

• Step 3: Confirm that the factored expression matches one of the given answer choices.

Now, let's work through each step:
Step 1: The coefficients of the terms $99ab^2$ and $81b$ are 99 and 81, respectively. The greatest common factor of these coefficients is 9.
Step 2: Both terms, $99ab^2$ and $81b$, contain the variable $b$. We can factor out $b$ as well. Thus, the GCF of both terms in the expression $99ab^2 + 81b$ is $9b$.
Step 3: Factor $9b$ out of both terms:
$\begin{aligned} 99ab^2 + 81b &= 9b( \frac{99ab^2}{9b} + \frac{81b}{9b} )\\ &= 9b(11ab + 9) \end{aligned}$
Therefore, the equivalent expression to the given algebraic expression is $9b(11ab + 9)$. This matches choice 2.

Thus, the solution to the problem is $9b(11ab + 9)$.