It looks like you're dealing with the expression $(2x + 3y)^2$. This expression can be expanded using the formula for the square of a binomial:

$(a + b)^2 = a^2 + 2ab + b^2$

In this case, $a = 2x$ and $b = 3y$. Let's apply the formula:

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

Now, calculate each term:

1. $(2x)^2 = 4x^2$
2. $2(2x)(3y) = 12xy$
3. $(3y)^2 = 9y^2$

So, the expanded form of $(2x + 3y)^2$ is:

$\boxed{4x^2 + 12xy + 9y^2}$

Would you like more details or have any questions about this expansion? Here are some related questions:

1. How do you expand $(2x - 3y)^2$?
2. What is the formula for the square of a binomial, and why does it work?
3. Can you expand $(3x + 4y)^2$ using the same method?
4. How do you factor the expression $4x^2 + 12xy + 9y^2$ back into $(2x + 3y)^2$?
5. How does the expansion change if you have $(2x + 3y)^3$ instead?
6. What happens when you expand $(2x - 3y)(2x + 3y)$?
7. Can you expand the expression $(x + y + z)^2$?
8. How do you apply the binomial theorem to higher powers of binomials?

Tip: When expanding a binomial squared, remember that the middle term is always twice the product of the two terms in the binomial.