https://file.aiquickdraw.com/mathbot/file/1726673658044tely6t17.jpg

Let's perform the given operation: 

\[
(4x^2 - 10x) + (2x^2 + 5x - 5)
\]

### Step 1: Combine like terms
- For \(x^2\) terms: \(4x^2 + 2x^2 = 6x^2\)
- For \(x\) terms: \(-10x + 5x = -5x\)
- For constants: There is only \(-5\), which remains as it is.

### Final Answer:
\[
6x^2 - 5x - 5
\]

Would you like more details or explanations on any part?

Here are 5 related questions to expand on this:
1. How do you add or subtract polynomials?
2. What happens when there are no like terms to combine?
3. How would you multiply two binomials like \((4x - 5)(2x + 3)\)?
4. How do you factor quadratic expressions like \(6x^2 - 5x - 5\)?
5. How can this operation change if a different variable is used instead of \(x\)?

**Tip:** Always align like terms when adding or subtracting polynomials to ensure you're combining terms correctly!

Learn how to perform the operation by adding polynomials and combining like terms in (4x^2 - 10x) + (2x^2 + 5x - 5). This problem covers key algebraic concepts, suitable for students in Grades 8-10.

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