To expand $(5x + 4)^2$, we'll use the binomial expansion formula:

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

Here, $a = 5x$ and $b = 4$. Applying the formula:

$(5x + 4)^2 = (5x)^2 + 2(5x)(4) + 4^2$

Now, let's simplify:

$(5x)^2 = 25x^2$ $2(5x)(4) = 40x$ $4^2 = 16$

So, the expanded form is:

$(5x + 4)^2 = 25x^2 + 40x + 16$

Would you like further details or have any questions about this?

Here are some related questions you might find interesting:

1. How do you expand binomials with negative terms?
2. What is the FOIL method, and how does it relate to binomial expansion?
3. How can you factor quadratic expressions like $25x^2 + 40x + 16$?
4. What are some common algebraic identities and their uses?
5. How can you solve quadratic equations derived from binomial expansions?

Tip: When expanding binomials, remember the pattern of the squared terms to avoid mistakes.