3. \( 12\left(a+\frac{2}{3} b\right) \)

Did you know that simplifying expressions like \( 12\left(a+\frac{2}{3} b\right) \) helps you understand the relationship between numbers and variables better? When you distribute the 12, you get \( 12a + 8b \). This is a common technique in algebra that prepares you for solving equations and inequalities! When tackling expressions, it’s key to watch out for common mistakes, such as forgetting to multiply the coefficient with all parts inside the parentheses. Always double-check your work! Instead of \( 12\left(a + \frac{2}{3} b\right) \) turning into \( 12a + 2b \)—which is incorrect—you must ensure that the fraction also gets multiplied properly. Happy simplifying!