To simplify \((2x + 1)(2x - 3)\), we can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last):

1. **First terms**: \(2x \times 2x = 4x^2\)
2. **Outer terms**: \(2x \times -3 = -6x\)
3. **Inner terms**: \(1 \times 2x = 2x\)
4. **Last terms**: \(1 \times -3 = -3\)

Now, combine the terms:
\[
4x^2 - 6x + 2x - 3 = 4x^2 - 4x - 3
\]

Thus, the simplified expression is:
\[
4x^2 - 4x - 3
\]

Would you like further explanation or details on this?

Here are 5 related questions:
1. How would you factor \(4x^2 - 4x - 3\)?
2. What are the roots of the equation \(4x^2 - 4x - 3 = 0\)?
3. How do you apply the distributive property to polynomials?
4. What are common mistakes to avoid when using the FOIL method?
5. How would the expression change if it were \((2x + 1)^2\) instead?

**Tip**: Always double-check the signs when using FOIL, especially in the outer and inner terms.

Learn how to simplify the polynomial expression (2x + 1)(2x - 3) using the FOIL method. This step-by-step explanation covers polynomial multiplication and the distributive property. Suitable for students in Grades 7-9.

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