https://file.aiquickdraw.com/mathbot/file/1729880246126lmr6qemt.jpg

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.

Learn how to expand and simplify the binomial expression (n + 6)(n - 3) using polynomial expansion. This example helps students in Grades 7-10 practice basic algebra skills by applying the distributive property (FOIL method).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation