Factorize the expression: 8xy3 + 12xy2

The expression is $8xy^3 + 12xy^2$.
The terms are $8xy^3$ and $12xy^2$.

First, find the GCF of the numerical coefficients: 8 and 12.
The GCF of 8 and 12 is 4.

Next, find the GCF of the variables.
For $x$: Both terms contain $x$. The lowest power of $x$ is $x^1$. So, $x$ is a common factor.
For $y$: Both terms contain $y$. The lowest power of $y$ is $y^2$ (from $12xy^2$). So, $y^2$ is a common factor.

The overall GCF for the expression is $4xy^2$.

Divide each term by the GCF, $4xy^2$:

$$\frac{8xy^3}{4xy^2} = 2y$$ $$\frac{12xy^2}{4xy^2} = 3$$

Combine the GCF with the results from Step 2.

$$4xy^2(2y + 3)$$