Let's solve the expression:

\[
(3x^2 - 3x + 9) + (-5x^2 - 8x - 7)
\]

1. Combine the like terms:

- \(3x^2\) and \(-5x^2\)
- \(-3x\) and \(-8x\)
- \(9\) and \(-7\)

2. Perform the addition:

\[
(3x^2 - 5x^2) + (-3x - 8x) + (9 - 7)
\]

\[
= -2x^2 - 11x + 2
\]

Thus, the simplified expression is:

\[
-2x^2 - 11x + 2
\]

Would you like more details on any step?

Here are 5 related questions you might find interesting:
1. How do you add polynomials with different degrees?
2. What is the significance of combining like terms?
3. How do you factor a quadratic expression like \(-2x^2 - 11x + 2\)?
4. How do you solve quadratic equations?
5. How do you perform polynomial long division?

**Tip:** Always align like terms vertically when adding or subtracting polynomials to avoid mistakes.

(3x^2 − 3x + 9) + (−5x^2 − 8x − 7)

Learn how to simplify the polynomial expression (3x^2 − 3x + 9) + (−5x^2 − 8x − 7) by combining like terms. This guide walks through the algebraic process of adding polynomials and clarifies key concepts such as combining like terms, polynomial addition, and algebraic simplifications. Suitable for students in Grades 8-10.

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