The expression you've provided is \((n - 7)(n + 6)\). This is a product of two binomials and can be expanded using the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last).

### Solution:
Let's expand the expression:

\[
(n - 7)(n + 6)
\]

1. **First:** Multiply the first terms in each binomial:
   \[
   n \times n = n^2
   \]

2. **Outer:** Multiply the outer terms:
   \[
   n \times 6 = 6n
   \]

3. **Inner:** Multiply the inner terms:
   \[
   -7 \times n = -7n
   \]

4. **Last:** Multiply the last terms:
   \[
   -7 \times 6 = -42
   \]

Now, combine all these results:

\[
n^2 + 6n - 7n - 42
\]

Finally, combine like terms:

\[
n^2 - n - 42
\]

So, the expanded form of \((n - 7)(n + 6)\) is \(n^2 - n - 42\).

Would you like more details or have any questions?

### Related Questions:
1. How do you factor the expression \( n^2 - n - 42 \) back into its binomial form?
2. What is the significance of the FOIL method in expanding binomials?
3. Can you apply the distributive property to a trinomial multiplied by a binomial?
4. How do you solve the equation \( n^2 - n - 42 = 0 \)?
5. What are some common mistakes to avoid when expanding binomials?

**Tip:** When expanding binomials, carefully combine like terms to ensure accuracy. This step is crucial, especially when dealing with more complex expressions.

Learn how to expand the expression (n - 7)(n + 6) using the FOIL method step-by-step. This problem covers key algebraic concepts, including binomial expansion and the FOIL method. Suitable for students in Grades 7-9.

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