To expand $(4a + 4b)^2$, we can apply the square of a binomial formula, which states:

$(x + y)^2 = x^2 + 2xy + y^2$

In this case, $x = 4a$ and $y = 4b$. Using the formula:

$(4a + 4b)^2 = (4a)^2 + 2(4a)(4b) + (4b)^2$

Now, let's calculate each term:

1. $(4a)^2 = 16a^2$
2. $2(4a)(4b) = 32ab$
3. $(4b)^2 = 16b^2$

So, the expanded form is:

$(4a + 4b)^2 = 16a^2 + 32ab + 16b^2$

Would you like further details or have any other questions? Here are a few related questions you might find useful:

1. How do you expand binomials with different powers?
2. What is the significance of the square of a binomial in algebra?
3. How do you factor expressions like $16a^2 + 32ab + 16b^2$?
4. What are other binomial identities in algebra?
5. How do you simplify polynomial expressions like this?

Tip: Remember that the square of a binomial involves squaring each term and adding twice the product of both terms.