https://file.aiquickdraw.com/mathbot/file/1728968769188o3tmez6x.jpg

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.

Learn how to simplify the polynomial expression (x^2 - 6x + 6) - (x^2 - 4) by distributing and combining like terms. This problem involves key algebraic concepts and is suitable for students in Grades 7-9.

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