We need to factor the expression $9m^5n^2 + 12m^3n^3$.

1. Problem Description

We need to factor the expression $9m^5n^2 + 12m^3n^3$.

2. Solution Steps

First, we find the greatest common factor (GCF) of the coefficients 9 and

1

2. The GCF of 9 and 12 is

3.

Next, we find the lowest power of $m$ in both terms. The terms are $m^5$ and $m^3$. The lowest power is $m^3$.

Then, we find the lowest power of $n$ in both terms. The terms are $n^2$ and $n^3$. The lowest power is $n^2$.

Therefore, the GCF of the entire expression is $3m^3n^2$.

Now, we factor out the GCF from each term:

$9m^5n^2 = (3m^3n^2)(3m^2)$

$12m^3n^3 = (3m^3n^2)(4n)$

So, we have:

$9m^5n^2 + 12m^3n^3 = (3m^3n^2)(3m^2) + (3m^3n^2)(4n)$

$9m^5n^2 + 12m^3n^3 = 3m^3n^2(3m^2 + 4n)$

3. Final Answer

The factored expression is $3m^3n^2(3m^2 + 4n)$.