## Simplifying the Expression: (9x^2 - 9x - 7) - (x^2 - 6x - 2)

This expression involves subtracting two polynomials. To simplify it, we need to follow the order of operations and distribute the negative sign.

**Step 1: Distribute the negative sign**

Remember that subtracting a polynomial is the same as adding its opposite.

(9x^2 - 9x - 7) + **(-1)** (x^2 - 6x - 2)

Now we multiply each term inside the second parenthesis by -1:

(9x^2 - 9x - 7) + (-x^2 + 6x + 2)

**Step 2: Combine like terms**

Identify terms with the same variable and exponent, then combine their coefficients:

(9x^2 - x^2) + (-9x + 6x) + (-7 + 2)

**Step 3: Simplify**

8x^2 - 3x - 5

**Therefore, the simplified expression is 8x^2 - 3x - 5.**