Certainly! Let's simplify the given expression [tex]\(\left(-x^3 - y^3 + z^2 \right) + (x - y)\)[/tex] step by step.
1. Expand the expression inside the parentheses:
The expression given is [tex]\(\left(-x^3 - y^3 + z^2 \right) + (x - y)\)[/tex].
2. Combine the two parts:
When we combine [tex]\(-x^3 - y^3 + z^2\)[/tex] with [tex]\(x - y\)[/tex], we write it as:
[tex]\[
-x^3 - y^3 + z^2 + x - y
\][/tex]
3. Group like terms together if necessary:
Looking at the expression [tex]\(-x^3 - y^3 + z^2 + x - y\)[/tex]:
- The terms [tex]\(-x^3\)[/tex] and [tex]\(-y^3\)[/tex] are cubic terms of the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], respectively.
- The term [tex]\(z^2\)[/tex] is a square term of the variable [tex]\(z\)[/tex].
- The term [tex]\(x\)[/tex] is a linear term of [tex]\(x\)[/tex].
- The term [tex]\(-y\)[/tex] is a linear term of [tex]\(y\)[/tex].
4. Simplify (if possible):
Since there are no like terms to combine further, we have the simplified expression as:
[tex]\[
-x^3 - y^3 + z^2 + x - y
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[
-x^3 - y^3 + z^2 + x - y
\][/tex]
This is the final answer.
