Sure! Let's break down and analyze the expression [tex]\( x^4 - (x - z) \)[/tex] step-by-step:
1. Understand the expression:
We're given [tex]\( x^4 - (x - z) \)[/tex]. Here, [tex]\( x \)[/tex] and [tex]\( z \)[/tex] are variables.
2. Distribute the negative sign:
When we subtract a term in parentheses, we need to distribute the negative sign to each term inside the parentheses. This means:
[tex]\[
x^4 - (x - z) = x^4 - x + z
\][/tex]
So, the negative sign affects both the [tex]\( x \)[/tex] and the [tex]\( -z \)[/tex] inside the parentheses, turning [tex]\( -x \)[/tex] to [tex]\( -x \)[/tex] and [tex]\( -(-z) \)[/tex] to [tex]\( +z \)[/tex].
3. Combine the terms:
Now combine all our terms into a single expression:
[tex]\[
x^4 - x + z
\][/tex]
Thus, the final simplified and distributed version of the given expression [tex]\( x^4 - (x - z) \)[/tex] is:
[tex]\[
x^4 - x + z
\][/tex]
