To expand and simplify $(n + 6)(n - 3)$, we'll apply the distributive property (also known as FOIL, for First, Outer, Inner, Last):

$(n + 6)(n - 3) = n(n) + n(-3) + 6(n) + 6(-3)$

Now, let's expand it step by step:

• $n \times n = n^2$
• $n \times (-3) = -3n$
• $6 \times n = 6n$
• $6 \times (-3) = -18$

Now, combine all the terms:

$n^2 - 3n + 6n - 18$

Simplify by combining like terms:

$n^2 + 3n - 18$

Thus, the expanded and simplified form is:

$n^2 + 3n - 18$

Would you like any further clarification or details?

Here are 5 related questions you could explore:

1. How would you factor $n^2 + 3n - 18$ back into its original form?
2. What happens when you expand and simplify $(n + 4)(n - 5)$?
3. How can you use the FOIL method on binomials with higher degree terms?
4. Can you expand and simplify $(n + a)(n - b)$ with arbitrary constants $a$ and $b$?
5. How does expanding and simplifying help solve quadratic equations?

Tip: Always combine like terms carefully after expansion to ensure accuracy in simplifying expressions.