To simplify the given expression:

\[
2x(-2x - y) - (x^2 - 4xy)
\]

Let's first distribute and then combine like terms.

### Step 1: Distribute 

Distribute \(2x\) in the first term:

\[
2x(-2x) + 2x(-y) = -4x^2 - 2xy
\]

So, the expression becomes:

\[
-4x^2 - 2xy - (x^2 - 4xy)
\]

### Step 2: Distribute the negative sign

Now distribute the negative sign across the second group:

\[
-4x^2 - 2xy - x^2 + 4xy
\]

### Step 3: Combine like terms

Combine all like terms:

- The \(x^2\) terms: \(-4x^2 - x^2 = -5x^2\)
- The \(xy\) terms: \(-2xy + 4xy = 2xy\)

Thus, the simplified expression is:

\[
\boxed{-5x^2 + 2xy}
\]

Would you like more details, or do you have any questions? Here are some related questions to consider:

1. How do you factor a quadratic expression like \(-5x^2 + 2xy\)?
2. What is the difference between distributing and factoring in algebra?
3. How do you solve for \(x\) and \(y\) if given a specific value for one variable?
4. What are like terms, and why is it important to combine them?
5. How does distributing a negative sign affect the terms in an expression?

**Tip:** When simplifying expressions, carefully apply the distributive property and combine like terms step by step to avoid mistakes.

Simplify the algebraic expression 2x(-2x - y) - (x^2 - 4xy) with a detailed step-by-step solution. This problem covers algebraic concepts such as the distributive property, combining like terms, and simplifying expressions. Suitable for students in Grades 9-11.

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