1. **State the problem:** Simplify the expression $12a^2b + 18ab^2 - 30ab$. 2. **Identify the common factors:** Each term contains the variables $a$ and $b$, and the coefficients 12, 18, and 30 have a greatest common divisor (GCD) of 6. 3. **Factor out the GCD and common variables:** $$6ab(2a + 3b - 5)$$ 4. **Explanation:** We took out $6ab$ because 6 is the GCD of the coefficients and $ab$ is common in all terms. 5. **Final answer:** $$6ab(2a + 3b - 5)$$