Let's simplify the given expression:

\[
(9x^2 - 9x - 7) - (x^2 - 6x - 2)
\]

First, distribute the negative sign across the second set of parentheses:

\[
9x^2 - 9x - 7 - x^2 + 6x + 2
\]

Now, combine like terms:

- Combine the \(x^2\) terms: \(9x^2 - x^2 = 8x^2\)
- Combine the \(x\) terms: \(-9x + 6x = -3x\)
- Combine the constant terms: \(-7 + 2 = -5\)

So, the simplified expression is:

\[
8x^2 - 3x - 5
\]

Would you like any more details or have any questions? Here are 5 related questions to further your understanding:

1. How would you factor the expression \(8x^2 - 3x - 5\)?
2. Can you solve the equation \(8x^2 - 3x - 5 = 0\) using the quadratic formula?
3. What is the vertex form of the quadratic expression \(8x^2 - 3x - 5\)?
4. How would you graph the quadratic function \(y = 8x^2 - 3x - 5\)?
5. How do you complete the square for the expression \(8x^2 - 3x - 5\)?

**Tip:** Always remember to distribute negative signs carefully when simplifying expressions.

Learn how to simplify the algebraic expression (9x^2 - 9x - 7) - (x^2 - 6x - 2) step-by-step. This problem involves simplifying polynomials using the distributive property. Suitable for students in Grades 7-9.

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