To simplify the expression \((4n - 3)(3n - 2)\), we apply the distributive property (also known as the FOIL method for binomials):

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

Now simplify each term:
1. \( 4n \times 3n = 12n^2 \)
2. \( 4n \times -2 = -8n \)
3. \( -3 \times 3n = -9n \)
4. \( -3 \times -2 = 6 \)

Now, combine all these terms:
\[
12n^2 - 8n - 9n + 6
\]

Combine the like terms \(-8n - 9n\):
\[
12n^2 - 17n + 6
\]

So, the simplified expression is:
\[
12n^2 - 17n + 6
\]

Would you like further details or have any questions?

Here are some related questions:
1. How do you expand binomials using the distributive property?
2. What is the FOIL method and when do you use it?
3. How do you simplify quadratic expressions?
4. How do you factor a quadratic expression like \(12n^2 - 17n + 6\)?
5. How do like terms affect simplification?

**Tip:** Always combine like terms to simplify expressions efficiently!

Learn how to simplify the expression (4n - 3)(3n - 2) step-by-step using the distributive property or FOIL method. This problem explores algebraic concepts such as binomial multiplication and simplification. Suitable for students in Grades 8-10.

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