https://file.aiquickdraw.com/mathbot/file/17260566571694b7rjklf.jpg

The expression in the image is:

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

Let's simplify this expression step-by-step:

1. Combine like terms (group terms with \(x^2\) and constants separately):
   \[
   (-x^2 + 2x^2) + (-2 + 1)
   \]

2. Simplify the \(x^2\) terms:
   \[
   (-1 + 2)x^2 = x^2
   \]

3. Simplify the constants:
   \[
   -2 + 1 = -1
   \]

Thus, the simplified expression is:
\[
x^2 - 1
\]

Would you like further details or have any questions?

Here are 5 related questions to further explore this topic:
1. How do you factor the expression \(x^2 - 1\)?
2. What is the graphical interpretation of \(x^2 - 1\)?
3. How can this type of simplification be applied in solving equations?
4. What happens if you introduce a higher degree polynomial into the expression?
5. Can you generalize the steps for simplifying any polynomial expression?

**Tip**: Always check for common factors or special forms, such as the difference of squares, when simplifying expressions like \(x^2 - 1\).

Simplify the expression (-x^2 - 2) + (2x^2 + 1).

Learn how to simplify the expression (-x^2 - 2) + (2x^2 + 1) by combining like terms. The step-by-step solution covers essential algebraic concepts and is suitable for students in Grades 8-10.

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