To simplify the expression [tex]\((4x - 4) - 8x\)[/tex], let's go through it step-by-step.
1. Distribute the negative sign: When we have a subtraction, we'll distribute the minus sign across the terms within the parentheses following it.
[tex]\[
(4x - 4) - 8x \implies 4x - 4 - 8x
\][/tex]
2. Combine the like terms: Combine the terms that contain [tex]\(x\)[/tex] and the constant terms separately.
[tex]\[
4x - 8x - 4
\][/tex]
3. Simplify the terms involving [tex]\(x\)[/tex]: Subtract [tex]\(8x\)[/tex] from [tex]\(4x\)[/tex]:
[tex]\[
4x - 8x = -4x
\][/tex]
4. Bring down the constant term: Now, we have:
[tex]\[
-4x - 4
\][/tex]
The expression [tex]\((4x - 4) - 8x\)[/tex] simplifies to [tex]\(-4x - 4\)[/tex].
Therefore, the correct answer is:
C. [tex]\(-4x - 4\)[/tex]
