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Let's simplify the given polynomial expression:

\[
\left( 7x^2 + x - 8 \right) - \left( -2x^2 - 8 \right)
\]

### Step-by-step solution:

1. **Distribute the negative sign** in front of the second expression:

\[
(7x^2 + x - 8) - (-2x^2 - 8) = 7x^2 + x - 8 + 2x^2 + 8
\]

2. **Combine like terms**:
   - For \(x^2\) terms: \(7x^2 + 2x^2 = 9x^2\)
   - For the constant terms: \(-8 + 8 = 0\)
   - For the linear term: \(x\) remains as is.

So the simplified expression is:

\[
9x^2 + x
\]

### Final Answer:
The equivalent expression is \(9x^2 + x\), which corresponds to option **C**.

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Do you want more details on any step?  
Here are some related questions:

1. How do you distribute a negative sign over a polynomial?
2. What are like terms and how do you combine them?
3. How can we handle polynomials with multiple variables?
4. What is the importance of simplifying expressions in algebra?
5. Can polynomial expressions always be factored?

**Tip**: Always distribute negative signs carefully to avoid errors in simplifying polynomials.

Simplify the following polynomial expression: (7x^2 + x - 8) - (-2x^2 - 8). Which expression is equivalent?

Simplify the polynomial expression (7x^2 + x - 8) - (-2x^2 - 8) using algebraic techniques. Learn how to distribute a negative sign and combine like terms to arrive at the simplified form 9x^2 + x. Suitable for Grades 8-10.

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