Let's solve the expression \((3h - 2)(3h - 4)\) by expanding it using the distributive property (also known as FOIL: First, Outer, Inner, Last):

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

Now, calculate each part:

- First: \(3h \times 3h = 9h^2\)
- Outer: \(3h \times -4 = -12h\)
- Inner: \(-2 \times 3h = -6h\)
- Last: \(-2 \times -4 = 8\)

Now, combine like terms:

\[
9h^2 - 12h - 6h + 8 = 9h^2 - 18h + 8
\]

So, the expanded form is:

\[
9h^2 - 18h + 8
\]

Would you like further details on any step? Here are 5 related questions to explore further:

1. What is the distributive property and how is it used in algebra?
2. Can you expand other expressions like \((2x + 3)(x - 5)\)?
3. How do you factor quadratic expressions like \(9h^2 - 18h + 8\)?
4. How does the FOIL method apply to binomial multiplication?
5. What are some applications of expanding binomials in real-world problems?

**Tip:** Always double-check for common factors when simplifying or expanding expressions!

Learn how to expand and simplify the binomial expression (3h–2)(3h–4) using the distributive property (FOIL method). This step-by-step guide breaks down key algebraic concepts, including binomial multiplication and quadratic expressions. Suitable for students in Grades 8-10.

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