Let's expand the expression $(3 + n)(5n + 6)$ using the distributive property (also known as FOIL for binomials).

1. First, multiply $3$ by each term in the second binomial: $3 \cdot 5n = 15n$ $3 \cdot 6 = 18$

2. Next, multiply $n$ by each term in the second binomial: $n \cdot 5n = 5n^2$ $n \cdot 6 = 6n$

Now, combine all the terms: $5n^2 + 15n + 6n + 18$

Simplify the like terms ($15n + 6n$): $5n^2 + 21n + 18$

So, the expanded form is: $5n^2 + 21n + 18$

Would you like more details on any part of this process or have any other questions?

Here are 5 related questions you might explore:

1. How do you factor a quadratic expression like $5n^2 + 21n + 18$?
2. What is the distributive property in algebra?
3. How can you solve quadratic equations like $5n^2 + 21n + 18 = 0$?
4. What is the difference between binomial and polynomial expansions?
5. How can FOIL be applied to binomials?

Tip: When expanding binomials, carefully organize your terms to ensure you combine like terms correctly.