1. **State the problem:** Simplify the algebraic expression $10a - 5a - 2 + a + 10a$. 2. **Identify like terms:** Like terms are terms that contain the same variable raised to the same power. Here, the like terms are $10a$, $-5a$, $a$, and $10a$. The constant term is $-2$. 3. **Combine like terms:** $$10a - 5a + a + 10a = (10 - 5 + 1 + 10)a = 16a$$ 4. **Write the simplified expression:** $$16a - 2$$ 5. **Final answer:** The simplified form of the expression is $16a - 2$.