To solve \((x + 6)(x - 2)\), we can expand the expression using the distributive property (also known as FOIL for binomials). Here's the step-by-step process:

\[
(x + 6)(x - 2) = x(x - 2) + 6(x - 2)
\]

Now, let's distribute:

\[
x(x - 2) = x^2 - 2x
\]
\[
6(x - 2) = 6x - 12
\]

Now, add the two results together:

\[
x^2 - 2x + 6x - 12
\]

Combine like terms:

\[
x^2 + 4x - 12
\]

Thus, the expanded form of \((x + 6)(x - 2)\) is:

\[
x^2 + 4x - 12
\]

Would you like further details on any part of this process?

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Here are 5 related questions to expand on this:

1. How do you factor quadratic expressions like \(x^2 + 4x - 12\)?
2. Can you solve the equation \((x + 6)(x - 2) = 0\)?
3. What are the roots of the quadratic equation \(x^2 + 4x - 12 = 0\)?
4. How do you complete the square for an equation like \(x^2 + 4x - 12\)?
5. What is the vertex form of the quadratic equation \(x^2 + 4x - 12\)?

**Tip**: Always combine like terms after distributing to simplify expressions properly.

Learn how to expand and simplify the algebraic expression (x+6)(x-2) using the distributive property. This step-by-step solution covers binomial expansion and combining like terms, making it suitable for students in Grades 8-10.

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