Let's solve the expression step by step:

We are given the expression:

\[
(3x^2 + 5x - 10) + (x^2 + 5x - 2)
\]

1. **Combine like terms:**
   - Combine the \(x^2\) terms: \(3x^2 + x^2 = 4x^2\)
   - Combine the \(x\) terms: \(5x + 5x = 10x\)
   - Combine the constant terms: \(-10 - 2 = -12\)

2. **Final simplified expression:**
   \[
   4x^2 + 10x - 12
   \]

Would you like further details or explanations on any part of the process?

Here are 5 related questions:
1. How would you solve for \(x\) in \(4x^2 + 10x - 12 = 0\)?
2. How do you factor a quadratic expression like \(4x^2 + 10x - 12\)?
3. What is the significance of combining like terms in algebraic expressions?
4. How can you graph the equation \(y = 4x^2 + 10x - 12\)?
5. Can this expression be simplified further through factoring or other methods?

**Tip:** Always double-check your steps when combining like terms to avoid errors!

Learn how to simplify the quadratic expression (3x^2 + 5x - 10) + (x^2 + 5x - 2) by combining like terms. This solution covers fundamental algebraic concepts like combining quadratic, linear, and constant terms. Suitable for students in Grades 7-9.

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