Certainly! Let's go through the process of simplifying the given expression step-by-step.
We're given the expression:
[tex]\[ (-x^3 - y^3 + x^2) + (x - y) \][/tex]
Step 1: Distribute any terms and combine like terms, if possible.
Firstly, we can write down all the terms from both groups:
[tex]\[ -x^3 - y^3 + x^2 + x - y \][/tex]
Step 2: Group the terms that are similar.
Group the terms involving [tex]\( x \)[/tex]:
[tex]\[ -x^3 + x^2 + x \][/tex]
Group the terms involving [tex]\( y \)[/tex]:
[tex]\[ -y^3 - y \][/tex]
There are no like terms to combine in each individual group, but we've organized the expression.
Step 3: Combine the groups back together to form one simplified expression.
The final simplified expression is:
[tex]\[ -x^3 + x^2 + x - y^3 - y \][/tex]
Thus, the simplified expression is:
[tex]\[ -x^3 + x^2 + x - y^3 - y \][/tex]
This is the simplest form of the given expression.
