The expanded form of the expression $3(x + 4)$ is $3x + 12$.

To expand the expression $3(x + 4)$, we utilize the distributive property of multiplication over addition. This property states that for any numbers $a$, $b$, and $c$, the equation $a(b + c)$ is equivalent to $ab + ac$. In our case, the number $3$ is multiplied by each term inside the parentheses: $x$ and $4$.

First, we multiply $3$ by $x$, which yields $3x$. Next, we multiply $3$ by $4$, resulting in $12$. When we combine these two products, we arrive at the expression $3x + 12$. This process is known as expanding because it transforms a compact expression into a more detailed form.

Mastering the expansion of expressions is a crucial skill in algebra. It not only aids in simplifying and solving equations but also facilitates the handling of more complex mathematical problems. By practicing this skill, you will gain confidence in manipulating algebraic expressions and prepare yourself for more advanced topics in mathematics.