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.