Let's solve the expression $(2x - 3)^2 - 4(2x - 3) - 5$.

Step 1: Expand $(2x - 3)^2$

Using the formula $(a - b)^2 = a^2 - 2ab + b^2$:

$(2x - 3)^2 = (2x)^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9$

Step 2: Expand $-4(2x - 3)$

Distribute the $-4$ to both terms:

$-4(2x - 3) = -8x + 12$

Step 3: Combine everything

Now substitute back into the original expression:

$(2x - 3)^2 - 4(2x - 3) - 5 = (4x^2 - 12x + 9) + (-8x + 12) - 5$

Step 4: Simplify

Combine like terms:

$4x^2 - 12x - 8x + 9 + 12 - 5 = 4x^2 - 20x + 16$

So the simplified expression is:

$4x^2 - 20x + 16$

Let me know if you'd like further details on any of the steps!

Related questions:

1. How do you factor quadratic expressions like $4x^2 - 20x + 16$?
2. Can you solve $4x^2 - 20x + 16 = 0$ for $x$?
3. What is the vertex form of a quadratic equation, and how do you convert $4x^2 - 20x + 16$ into that form?
4. How can you complete the square for $4x^2 - 20x + 16$?
5. What are the general steps for expanding binomials raised to a power?

Tip:

When simplifying expressions, always combine like terms and pay attention to negative signs to avoid mistakes.