To simplify $(3n + 1)(4n + 4)$, we can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last) for binomials. Here’s the step-by-step process:

$(3n + 1)(4n + 4) = (3n \cdot 4n) + (3n \cdot 4) + (1 \cdot 4n) + (1 \cdot 4)$

Now simplify each term:

1. $3n \cdot 4n = 12n^2$
2. $3n \cdot 4 = 12n$
3. $1 \cdot 4n = 4n$
4. $1 \cdot 4 = 4$

Now, combine like terms:

$12n^2 + 12n + 4n + 4 = 12n^2 + 16n + 4$

So, the simplified expression is:

$12n^2 + 16n + 4$

Would you like more details on the steps, or do you have any questions?

Here are 5 related questions you might find helpful:

1. How do you expand the product of two binomials?
2. What is the distributive property in algebra?
3. How do you combine like terms in an algebraic expression?
4. What are the common mistakes when expanding binomials?
5. Can the result $12n^2 + 16n + 4$ be factored further?

Tip: When expanding binomials, always remember to multiply each term in the first binomial by each term in the second one.