To factorize the expression \( y^2 + 3y + 2 \), we start by looking for two numbers that multiply to \( 2 \) (the constant term) and add up to \( 3 \) (the coefficient of \( y \)).

The two numbers that satisfy these conditions are \( 1 \) and \( 2 \), since:
\[
1 \times 2 = 2 \quad \text{and} \quad 1 + 2 = 3.
\]

So we can write:
\[
y^2 + 3y + 2 = (y + 1)(y + 2).
\]

Thus, the factorized form is:
\[
(y + 1)(y + 2).
\]

Would you like more details or have any questions?

Here are some related questions for practice:
1. Factorize \( y^2 + 5y + 6 \).
2. Factorize \( y^2 + 4y + 4 \).
3. Factorize \( y^2 - y - 6 \).
4. Factorize \( y^2 + 6y + 9 \).
5. Factorize \( y^2 + 7y + 10 \).

**Tip:** Always check for pairs of numbers that add up to the middle term's coefficient and multiply to the constant term when factorizing quadratic expressions.

Learn how to factorize the quadratic expression y^2 + 3y + 2 with a clear, step-by-step explanation. This problem covers key algebraic concepts and the factoring method, ideal for students in Grades 7-9.

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