To simplify the given expression, we can follow a step-by-step approach. The expression to simplify is:

\[
-4x^2 + \frac{1}{2}x^3 - x^2
\]

### Step 1: Combine Like Terms
Identify and combine the like terms. In this case, \(-4x^2\) and \(-x^2\) are like terms because they both contain \(x^2\).

\[
-4x^2 - x^2 = -5x^2
\]

Now, we can rewrite the original expression:

\[
-5x^2 + \frac{1}{2}x^3
\]

### Step 2: Reorder the Expression
To make it look more standard, you can reorder the terms by the degree of \(x\):

\[
\frac{1}{2}x^3 - 5x^2
\]

### Final Simplified Expression

\[
\frac{1}{2}x^3 - 5x^2
\]

This is the simplified form of the given expression.

Would you like more details or have any questions about this process?

### Follow-up Questions:

1. How would you factorize the expression \(\frac{1}{2}x^3 - 5x^2\)?
2. What are the roots of the equation \(\frac{1}{2}x^3 - 5x^2 = 0\)?
3. How would you graph the function \(f(x) = \frac{1}{2}x^3 - 5x^2\)?
4. How does the behavior of this function change as \(x\) approaches infinity or negative infinity?
5. Can you express this function as a product of its factors?

### Tip:
Always look for common factors when simplifying expressions. Combining like terms and factoring can often make complex expressions much easier to work with.

Learn how to simplify the expression -4x^2 + 1/2x^3 - x^2 using algebraic techniques. This problem involves combining like terms and reordering polynomial expressions. Suitable for Grades 7-9 students.

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