To expand and simplify the given expression $(n + 6)(n - 3)$, follow these steps:

Step 1: Apply the distributive property

Multiply each term in $(n + 6)$ by each term in $(n - 3)$: $(n + 6)(n - 3) = n \cdot n + n \cdot (-3) + 6 \cdot n + 6 \cdot (-3)$

Step 2: Perform the multiplications

$n \cdot n = n^2, \quad n \cdot (-3) = -3n, \quad 6 \cdot n = 6n, \quad 6 \cdot (-3) = -18$

Step 3: Combine all the terms

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

Step 4: Simplify by combining like terms

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

Final Answer:

The expanded and simplified form is: $n^2 + 3n - 18$

Would you like a detailed explanation of any step?

Here are 5 related questions you might consider:

1. How can the distributive property be applied to more complex polynomials?
2. What is the difference between expanding and factoring expressions?
3. How can the product of two binomials be visualized geometrically?
4. How does the FOIL method apply to multiplying binomials like $(n + 6)(n - 3)$?
5. What are the common mistakes to avoid when expanding polynomials?

Tip:

When simplifying expressions, always group like terms carefully to avoid errors in the final answer.