To solve the expression \((4x^2 - 8x + 5) - (-x^2 + 4x - 8)\), we need to distribute the negative sign across the second set of parentheses and then combine like terms.

### Step 1: Distribute the negative sign
\[
(4x^2 - 8x + 5) - (-x^2 + 4x - 8) = 4x^2 - 8x + 5 + x^2 - 4x + 8
\]

### Step 2: Combine like terms
- Combine the \(x^2\) terms: \(4x^2 + x^2 = 5x^2\)
- Combine the \(x\) terms: \(-8x - 4x = -12x\)
- Combine the constants: \(5 + 8 = 13\)

### Final simplified expression:
\[
5x^2 - 12x + 13
\]

Would you like more details or further clarification on any steps?

Here are 5 related questions you might want to explore:
1. How do you solve equations involving polynomial expressions?
2. Can you explain how to factor quadratic expressions?
3. What happens if you solve this expression for specific values of \(x\)?
4. How do you graph quadratic expressions like this one?
5. What is the difference between simplifying and factoring expressions?

**Tip:** Always double-check your sign changes, especially when distributing negatives across parentheses.

Learn how to simplify the polynomial expression (4x^2 - 8x + 5) - (-x^2 + 4x - 8) step by step by distributing the negative sign and combining like terms. This problem highlights key algebraic concepts, such as the distributive property and combining like terms. Suitable for students in Grades 7-9.

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