We will simplify \((2x - 1)^2 - 4x\) step by step:

### Step 1: Expand \((2x - 1)^2\)
\[
(2x - 1)^2 = (2x - 1)(2x - 1) = 4x^2 - 2x - 2x + 1 = 4x^2 - 4x + 1
\]

### Step 2: Substitute the expansion into the expression
\[
(2x - 1)^2 - 4x = 4x^2 - 4x + 1 - 4x
\]

### Step 3: Combine like terms
\[
4x^2 - 4x - 4x + 1 = 4x^2 - 8x + 1
\]

### Final Answer:
\[
4x^2 - 8x + 1
\]

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### Related Questions:
1. How do you factorize a quadratic expression like \(4x^2 - 8x + 1\)?
2. Can you expand and simplify \((3x + 2)^2 - 6x\)?
3. What is the vertex form of the quadratic \(4x^2 - 8x + 1\)?
4. How do you find the roots of \(4x^2 - 8x + 1\)?
5. What is the process of completing the square for \(4x^2 - 8x + 1\)?

### Tip:
Always group like terms and simplify step by step to avoid mistakes in algebraic manipulations.

Learn how to simplify the expression (2x - 1)^2 - 4x with a step-by-step breakdown. This solution covers expanding binomials, simplifying terms, and combining like terms. Suitable for students in Grades 7-9.

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