The given expression is:

$(x^2 - 6x + 6) - (x^2 - 4)$

Let's solve this step by step.

Step 1: Distribute the negative sign

We need to distribute the negative sign through the second parentheses: $(x^2 - 6x + 6) - x^2 + 4$

Step 2: Combine like terms

Now, combine the terms with $x^2$, $x$, and the constant terms:

• The $x^2$ terms: $x^2 - x^2 = 0$
• The $x$ terms: There is only $-6x$, so that remains as is.
• The constant terms: $6 + 4 = 10$

Final expression:

$-6x + 10$

Thus, the result of the operation is: $-6x + 10$

Would you like more details on any of the steps? Here are some follow-up questions to explore:

1. How do you distribute a negative sign across parentheses?
2. What are like terms, and why can we combine them?
3. What are the key differences between a binomial and a trinomial?
4. How do we interpret the coefficients of a polynomial?
5. Can we factor this expression further?

Tip: Always check if the result can be factored or simplified further, especially for factoring techniques like common factors.