1. The problem is to simplify the expression $ax - by$. 2. This expression is already in its simplest form because it is a linear combination of two variables $x$ and $y$ with coefficients $a$ and $b$ respectively. 3. There are no like terms to combine since $x$ and $y$ are different variables. 4. Therefore, the simplified form of the expression is simply: $$ax - by$$ This expression represents a linear expression in two variables.