To factor the expression \( y^2 + 10y + 21 \), we need to find two numbers that multiply to \( 21 \) (the constant term) and add up to \( 10 \) (the coefficient of the \( y \) term).
The numbers that satisfy this condition are \( 3 \) and \( 7 \), since:
- \( 3 \times 7 = 21 \)
- \( 3 + 7 = 10 \)
Thus, we can factor the expression as follows:
\[ y^2 + 10y + 21 = (y + 3)(y + 7) \]
So, the factored form of \( y^2 + 10y + 21 \) is
\[ (y + 3)(y + 7) \]