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Let's solve the expression step by step.

Given:
\[
-4(-2x^2 - x) - (x^2 - 2x + 9)
\]

### Step 1: Distribute the \(-4\) in the first part.
\[
-4(-2x^2 - x) = -4 \cdot (-2x^2) - 4 \cdot (-x) = 8x^2 + 4x
\]

### Step 2: Distribute the negative sign \(-\) in the second part.
\[
-(x^2 - 2x + 9) = -x^2 + 2x - 9
\]

### Step 3: Combine the results.
Now, add everything together:
\[
8x^2 + 4x - x^2 + 2x - 9
\]

### Step 4: Simplify by combining like terms.
\[
(8x^2 - x^2) + (4x + 2x) - 9 = 7x^2 + 6x - 9
\]

Thus, the simplified expression is:
\[
7x^2 + 6x - 9
\]

### Final Answer (in Bengali):
\[
7x^2 + 6x - 9
\]
এই সমীকরণের সরলীকৃত মান হল \( 7x^2 + 6x - 9 \)।

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Would you like more details, or do you have any other questions?

Here are 5 related questions:
1. How do you factor quadratic expressions like \(7x^2 + 6x - 9\)?
2. What are some methods to solve quadratic equations?
3. How does distributing a negative sign work in algebra?
4. How do you combine like terms in polynomials?
5. What is the significance of quadratic expressions in real-life problems?

**Tip:** Always remember to simplify the expression by distributing and combining like terms carefully.

Learn how to simplify the polynomial expression -4(-2x^2 - x) - (x^2 - 2x + 9) using the distributive property and combining like terms. Suitable for students in Grades 7-10.

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