To factor the expression \( y^2 + 7y + 10 \), we need to find two numbers that add up to \( 7 \) (the coefficient of \( y \)) and multiply to \( 10 \) (the constant term).
The two numbers that satisfy these conditions are \( 2 \) and \( 5 \) because:
- \( 2 + 5 = 7 \)
- \( 2 \times 5 = 10 \)
Now we can write the factored form of the expression as:
\[ (y + 2)(y + 5) \]
So, the factored form of \( y^2 + 7y + 10 \) is:
\[ (y + 2)(y + 5) \]