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.