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.

Learn how to expand the expression (2x + 3y)^2 using the binomial theorem with a detailed step-by-step solution. This problem covers key algebraic concepts, including binomial expansion and the application of the binomial theorem. Suitable for students in Grades 10-12.

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