$$ -\left(x-7\right)\left(x+7\right)-\left(x+6\right) $$

Let's simplify the expression:

\[
-\left(x - 7\right)\left(x + 7\right) - \left(x + 6\right)
\]

1. First, expand the product $\left(x - 7\right)\left(x + 7\right)$. This is a difference of squares:

\[
\left(x - 7\right)\left(x + 7\right) = x^2 - 49
\]

2. Now substitute this into the expression:

\[
-\left(x^2 - 49\right) - \left(x + 6\right)
\]

3. Distribute the negative sign:

\[
-x^2 + 49 - x - 6
\]

4. Combine like terms:

\[
-x^2 - x + 43
\]

So, the simplified expression is:

\[
-x^2 - x + 43
\]

Would you like to go over the details of any steps? Here are some related questions you might find interesting:

1. How do you expand a binomial product like $\left(x - a\right)\left(x + a\right)$?
2. What is the difference of squares, and how is it used in simplification?
3. How do you distribute a negative sign across a polynomial?
4. What are like terms, and how do you combine them?
5. How can you factor the expression $-x^2 - x + 43$?

**Tip:** When dealing with polynomials, always look for common patterns like the difference of squares or perfect square trinomials to simplify your work.

Learn how to simplify the expression -(x-7)(x+7) - (x+6) step-by-step. This problem involves algebraic simplification, focusing on the difference of squares formula. Suitable for high school students.

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