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The given problem asks to **simplify the expression and rewrite it in standard form**.

The expression is:
\[
2x(x - 1) - (2x - 1)(x + 1)
\]

Let's solve it step-by-step:

### Step 1: Expand both terms.
1. **Expanding \(2x(x - 1)\):**
   \[
   2x \cdot x - 2x \cdot 1 = 2x^2 - 2x
   \]

2. **Expanding \((2x - 1)(x + 1)\):**  
   Use the distributive property (FOIL):
   \[
   2x \cdot x + 2x \cdot 1 - 1 \cdot x - 1 \cdot 1 = 2x^2 + 2x - x - 1 = 2x^2 + x - 1
   \]

### Step 2: Write the full expression.
\[
2x^2 - 2x - (2x^2 + x - 1)
\]

### Step 3: Distribute the negative sign to the second term.
\[
2x^2 - 2x - 2x^2 - x + 1
\]

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

### Final Answer:
The simplified expression is:
\[
-3x + 1
\]

Thus, the correct answer is:
\[
\boxed{E) -3x + 1}
\]

---

Do you want further details or have any questions?

### 5 Related Questions:
1. How do you multiply binomials using the FOIL method?
2. What is the general form of a quadratic equation?
3. How can you quickly identify terms that cancel during simplification?
4. How do negative signs affect terms when expanding expressions?
5. What strategies are useful for checking polynomial expansions?

### Tip:
Always double-check signs when distributing or expanding terms, as small sign errors can lead to wrong results!

Simplify the expression 2x(x - 1) - (2x - 1)(x + 1) and write it in standard form.

Learn how to simplify the expression 2x(x - 1) - (2x - 1)(x + 1) in this detailed guide. This algebraic problem covers key concepts such as polynomial simplification and the use of the distributive property. Suitable for students in Grades 8-10.

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