Let's expand the expression \((3x + 4)(x - 2)\) using the distributive property (also known as FOIL for binomials):

\[
(3x + 4)(x - 2) = 3x(x) + 3x(-2) + 4(x) + 4(-2)
\]

Now, let's simplify each term:

1. \(3x(x) = 3x^2\)
2. \(3x(-2) = -6x\)
3. \(4(x) = 4x\)
4. \(4(-2) = -8\)

Now, combine all the terms:

\[
3x^2 - 6x + 4x - 8
\]

Simplify the middle terms:

\[
3x^2 - 2x - 8
\]

So, the expanded form is:

\[
3x^2 - 2x - 8
\]

Would you like more details on this expansion or have any questions?

Here are 5 related questions for further exploration:

1. How do you factor quadratic expressions like \(3x^2 - 2x - 8\)?
2. What is the FOIL method, and how does it apply to binomial multiplication?
3. How do you solve quadratic equations using factoring?
4. What is the difference between expanding and simplifying expressions?
5. How would you graph the quadratic equation \(y = 3x^2 - 2x - 8\)?

**Tip:** Always check if you can further simplify the expression after expanding or factoring for better clarity.

Explore the expansion of the binomial expression (3x + 4)(x - 2) using the FOIL method. This step-by-step solution explains how to apply the distributive property to expand and simplify the expression, resulting in the polynomial 3x^2 - 2x - 8. Suitable for students in Grades 8-10.

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