1. **State the problem:** Simplify the expression $Y - b - by - 1$. 2. **Identify like terms:** The terms are $Y$, $-b$, $-by$, and $-1$. Note that $Y$ and $y$ are different variables, so $Y$ and $-by$ cannot be combined. 3. **Rewrite the expression:** $$Y - b - by - 1$$ 4. **Group constants and terms with $b$:** $$Y - (b + by) - 1$$ 5. **Factor out $b$ from $b + by$:** $$Y - b(1 + y) - 1$$ 6. **Final simplified expression:** $$Y - b(1 + y) - 1$$ This is the simplest form unless you have values for $Y$, $b$, or $y$ to substitute.