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The factorized form of the expression $9y + 3$ is $3(3y + 1)$.

To factor an expression such as $9y + 3$, you first need to identify the greatest common factor (GCF) of the terms involved. In this case, the two terms are $9y$ and $3$. The GCF of $9$ and $3$ is $3$, as it is the largest number that divides both $9$ and $3$ without leaving a remainder.

Next, you divide each term of the expression by the GCF. For the term $9y$, dividing by $3$ results in $3y$. For the term $3$, dividing by $3$ yields $1$. Therefore, when you factor out the GCF (which is $3$), you are left with $3y + 1$ inside the parentheses.

Combining these elements, you write the GCF outside the parentheses and the simplified terms inside. This results in the factorized form $3(3y + 1)$ of the original expression $9y + 3$.

Mastering the process of factorization is an invaluable skill in algebra, as it simplifies equations and can facilitate their solution. Additionally, understanding factorization enhances your comprehension of the structure of algebraic expressions and aids in performing operations such as addition, subtraction, and multiplication of polynomials.