To expand the expression $(x + 3y)^2$, we use the binomial formula:

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

Here, $a = x$ and $b = 3y$. Substituting these into the formula, we get:

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

Now, simplify each term:

$x^2 + 6xy + 9y^2$

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

$x^2 + 6xy + 9y^2$

Would you like further details on this, or do you have any other questions?

Related Questions:

1. How would you expand and simplify $(x - 3y)^2$?
2. What is the general formula for expanding $(a + b)^2$?
3. How does the expansion change if the expression is $(2x + 3y)^2$?
4. What is the expansion of $(x + y)^3$ and how does it compare?
5. How can the expanded form $x^2 + 6xy + 9y^2$ be factored back into its original binomial form?

Tip: When dealing with binomial squares, remember to multiply the middle term (cross product) by 2, as it represents the sum of both cross products.