Let's expand the expression \((2x - 3)(2x + 2)\) using the distributive property (FOIL method).

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

1. **First**: Multiply the first terms in each binomial.
   \[
   2x \cdot 2x = 4x^2
   \]

2. **Outer**: Multiply the outer terms.
   \[
   2x \cdot 2 = 4x
   \]

3. **Inner**: Multiply the inner terms.
   \[
   -3 \cdot 2x = -6x
   \]

4. **Last**: Multiply the last terms in each binomial.
   \[
   -3 \cdot 2 = -6
   \]

Now, add all the results together:

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

Combine like terms (\(4x\) and \(-6x\)):

\[
\boxed{4x^2 - 2x - 6}
\]

This is the expanded form of the given expression.

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How would you factor the expression \(4x^2 - 2x - 6\) back into its original form?
2. Can you expand and simplify \((3x - 4)(x + 5)\)?
3. What happens if you multiply two binomials with the same terms, like \((2x - 3)(2x - 3)\)?
4. How do you apply the distributive property to expressions with more than two terms, like \((x + 1)(2x^2 - 3x + 4)\)?
5. How does the presence of negative terms affect the expansion of binomials?

**Tip:** When dealing with subtraction in binomials, be careful with the signs while multiplying the terms, especially during the Inner and Last steps.

Learn how to expand the expression (2x - 3)(2x + 2) using the FOIL method step-by-step. This problem covers polynomial multiplication techniques and the FOIL method, suitable for students in Grades 8-10.

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