The expression is:

\[
-(x^2 - 4x + 1) - (2x^2 + 9)
\]

Let's simplify it step by step.

1. First, distribute the negative signs:
   \[
   -x^2 + 4x - 1 - 2x^2 - 9
   \]

2. Combine like terms:
   - The \(x^2\) terms: \(-x^2 - 2x^2 = -3x^2\)
   - The constant terms: \(-1 - 9 = -10\)

So, the simplified expression is:

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

Would you like further details or clarifications?

Here are some related questions:
1. How would you factor a quadratic expression like this one?
2. Can you solve \(-3x^2 + 4x - 10 = 0\)?
3. What is the vertex of the quadratic function \(-3x^2 + 4x - 10\)?
4. How do you find the axis of symmetry for a quadratic equation?
5. What are the properties of parabolas when the coefficient of \(x^2\) is negative?

**Tip**: When combining like terms, always ensure you are working with the same variable or constant values to avoid mistakes.

Discover how to simplify the polynomial expression (−x^2 − 4x + 1)−(2x^2 + 9) step by step. This solution breaks down the use of the distributive property and combining like terms, making it suitable for students in Grades 8-10.

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