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.

Learn how to simplify the algebraic expression (2x - 3)^2 - 4(2x - 3) - 5 with a step-by-step breakdown. This guide explores expanding binomials, applying the distributive property, and combining like terms. Suitable for students in Grades 9-10.

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