Factor the given expression: $xy + 3y + 2x + 6$.

1. Problem Description

Factor the given expression: $xy + 3y + 2x + 6$.

2. Solution Steps

We can use factoring by grouping.

First, group the terms as follows:

$(xy + 3y) + (2x + 6)$

Now, factor out the greatest common factor (GCF) from each group.

From the first group, $xy + 3y$, the GCF is $y$. Factoring out $y$, we get $y(x + 3)$.

From the second group, $2x + 6$, the GCF is $2$. Factoring out $2$, we get $2(x + 3)$.

So, we have $y(x + 3) + 2(x + 3)$.

Now, we can factor out the common binomial factor $(x + 3)$ from the entire expression.

$(x + 3)(y + 2)$

3. Final Answer

$(x+3)(y+2)$