To expand \((2x + 2)^2\), use the formula for the square of a binomial:

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

In this case:
- \(a = 2x\)
- \(b = 2\)

Now, apply the formula:

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

Calculate each term:
1. \((2x)^2 = 4x^2\)
2. \(2 \cdot (2x) \cdot 2 = 8x\)
3. \(2^2 = 4\)

Now, combine all the terms:

\[
(2x + 2)^2 = 4x^2 + 8x + 4
\]

So, the expanded form is:

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

Would you like a more detailed explanation or have any questions?

Here are 5 related questions you might be interested in:
1. How do you expand \((3x + 4)^2\)?
2. What is the formula for the square of a difference, \((a - b)^2\)?
3. How do you factor the expression \(4x^2 + 8x + 4\) back into a binomial?
4. How can you apply the distributive property to expand \((2x + 2)(2x + 2)\)?
5. What is the geometric interpretation of squaring a binomial?

**Tip:** When expanding binomials, always apply the distributive property or binomial formulas carefully to avoid mistakes.

Learn how to expand (2x + 2)² step by step using the binomial formula. This solution breaks down the process, applying the formula (a + b)² = a² + 2ab + b² and providing detailed calculations. Perfect for students in Grades 8-10 studying algebra and polynomials.

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