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Let's simplify the given expression \((4x - 1)(2x - 2)\).

To expand this expression, we apply the distributive property (also known as the FOIL method for binomials):

\[
(4x - 1)(2x - 2) = (4x)(2x) + (4x)(-2) + (-1)(2x) + (-1)(-2)
\]

Now, calculate each term:

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

Now, combine all the terms:

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

Combine like terms (\(-8x - 2x = -10x\)):

\[
8x^2 - 10x + 2
\]

So, the simplified expression is:

\[
8x^2 - 10x + 2
\]

Would you like further details on any step, or have any questions? Here are five related questions you can explore:

1. How do you factor a quadratic expression like \(8x^2 - 10x + 2\)?
2. What is the FOIL method, and when is it applied?
3. How do you simplify expressions with more than two terms in each binomial?
4. How do you solve quadratic equations after simplification?
5. What other ways can binomials be expanded apart from the FOIL method?

**Tip:** Always check for common factors before expanding binomials, as it can simplify calculations!

Learn how to simplify the binomial expression (4x - 1)(2x - 2) using the distributive property (FOIL method). This problem demonstrates key algebraic concepts and is suitable for students in Grades 8-10.

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