To factor the quadratic expression \(x^2 + 6x + 9\) as the product of two binomials, we first look for two numbers that add up to the coefficient of \(x\) (which is 6) and multiply to the constant term (which is 9).
The numbers that meet these criteria are 3 and 3, since:
\[ 3 + 3 = 6 \] \[ 3 \times 3 = 9 \]
Thus, we can rewrite the quadratic expression using these numbers:
\[ x^2 + 6x + 9 = (x + 3)(x + 3) \]
This can also be expressed as:
\[ (x + 3)^2 \]
Therefore, the factored form of \(x^2 + 6x + 9\) is:
\[ \boxed{(x + 3)(x + 3)} \quad \text{or} \quad \boxed{(x + 3)^2} \]