Sure, let's simplify each of the given expressions step-by-step:
### 1. Simplify [tex]\((- \sqrt{x-4})^2\)[/tex]
To simplify [tex]\((- \sqrt{x-4})^2\)[/tex]:
[tex]\[
(- \sqrt{x-4})^2
\][/tex]
When you square a number, it becomes positive since [tex]\((a)^2 = a \times a\)[/tex].
[tex]\[
= (\sqrt{x-4})^2
\][/tex]
Now, the square and the square root will cancel each other out:
[tex]\[
= x - 4
\][/tex]
So, [tex]\((- \sqrt{x-4})^2\)[/tex] simplifies to:
[tex]\[
x - 4
\][/tex]
### 2. Simplify [tex]\(-x + 4\)[/tex]
The expression [tex]\(-x + 4\)[/tex] is already in its simplest form as there are no further operations that can simplify it:
[tex]\[
- x + 4
\][/tex]
### 3. Simplify [tex]\(x - 4\)[/tex]
The expression [tex]\(x - 4\)[/tex] is also already in its simplest form:
[tex]\[
x - 4
\][/tex]
### 4. Simplify [tex]\(2x - 8\)[/tex]
To simplify [tex]\(2x - 8\)[/tex], we look for a common factor:
We notice that 2 is a common factor:
[tex]\[
2x - 8 = 2(x - 4)
\][/tex]
So, [tex]\(2x - 8\)[/tex] can be factored as:
[tex]\[
2(x - 4)
\][/tex]
When simplified, these factors indicate that:
[tex]\[
2x - 8 = 2(x - 4)
\][/tex]
### Summary
1. [tex]\((- \sqrt{x-4})^2\)[/tex] simplifies to [tex]\(x - 4\)[/tex].
2. [tex]\(-x + 4\)[/tex] remains as [tex]\(-x + 4\)[/tex].
3. [tex]\(x - 4\)[/tex] remains as [tex]\(x - 4\)[/tex].
4. [tex]\(2x - 8\)[/tex] simplifies to [tex]\(2(x - 4)\)[/tex].
So, the simplified forms of the given expressions are:
1. [tex]\(x - 4\)[/tex]
2. [tex]\(-x + 4\)[/tex]
3. [tex]\(x - 4\)[/tex]
4. [tex]\(2(x - 4)\)[/tex].
