The expression \((2x + 2y)^2\) can be expanded using the square of a binomial formula:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, \( a = 2x \) and \( b = 2y \). Applying the formula:

\[
(2x + 2y)^2 = (2x)^2 + 2(2x)(2y) + (2y)^2
\]

Now calculate each term:

\[
(2x)^2 = 4x^2
\]
\[
2(2x)(2y) = 8xy
\]
\[
(2y)^2 = 4y^2
\]

So, the expansion of \((2x + 2y)^2\) is:

\[
4x^2 + 8xy + 4y^2
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you expand \((3x + 4y)^2\)?
2. Can you expand \((2x - 2y)^2\)?
3. How would you apply this expansion to solve an equation?
4. What happens if the binomial contains fractions, such as \(\left(\frac{x}{2} + \frac{y}{3}\right)^2\)?
5. How does the expansion change if there are more than two variables?

**Tip:** When expanding a binomial square, always focus on squaring each term individually and then multiplying the cross terms by 2!

Expand the binomial expression (2x + 2y)^2 using the binomial square formula. This problem explores key algebraic concepts, including binomial expansion and the binomial theorem. Suitable for students in Grades 8-10.

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