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.