Let's simplify the expression step by step:

\[
-2x(4x^2 + 2x - 5) + 4x(x^2 - 2)
\]

### Step 1: Distribute \(-2x\) across \((4x^2 + 2x - 5)\):
\[
-2x(4x^2) = -8x^3
\]
\[
-2x(2x) = -4x^2
\]
\[
-2x(-5) = 10x
\]

Thus, the first part becomes:
\[
-8x^3 - 4x^2 + 10x
\]

### Step 2: Distribute \(4x\) across \((x^2 - 2)\):
\[
4x(x^2) = 4x^3
\]
\[
4x(-2) = -8x
\]

Thus, the second part becomes:
\[
4x^3 - 8x
\]

### Step 3: Combine like terms:
Now, let's combine the results from Step 1 and Step 2:

\[
-8x^3 - 4x^2 + 10x + 4x^3 - 8x
\]

Combine the \(x^3\), \(x^2\), and \(x\) terms:

\[
(-8x^3 + 4x^3) = -4x^3
\]
\[
-4x^2
\]
\[
(10x - 8x) = 2x
\]

### Final simplified expression:
\[
-4x^3 - 4x^2 + 2x
\]

Let me know if you'd like more details or explanations. 

Here are some related questions for further practice:

1. What happens if you change the signs of all terms in the expression?
2. Can you factor the final expression \(-4x^3 - 4x^2 + 2x\)?
3. How would the expression change if one of the constants inside the parentheses were different?
4. What if the original expression included higher powers of \(x\)?
5. How would you graph the simplified expression?

**Tip**: Always group and combine like terms carefully when simplifying polynomials.

This guide explains how to simplify the polynomial expression -2x(4x^2 + 2x - 5) + 4x(x^2 - 2) step-by-step using the distributive property and combining like terms. Suitable for students in Grades 9-11, this problem covers key algebraic techniques for simplifying polynomials.

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