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.

Learn how to expand the expression (x + 3y)^2 using the binomial formula. This detailed solution covers step-by-step simplification and provides insights into algebraic expansion techniques. Suitable for Grades 7-9.

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