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!