9 - 6p + p2

A perfect square trinomial has the form $a^2 - 2ab + b^2 = (a-b)^2$.
In our expression, $p^2$ corresponds to $a^2$, so $a = p$.
The constant term 9 corresponds to $b^2$, so $b = \sqrt{9} = 3$.

The middle term of a perfect square trinomial should be $-2ab$.
Using $a=p$ and $b=3$, we calculate $-2ab = -2(p)(3) = -6p$.
This matches the middle term of the given expression, $-6p$.

Since it fits the perfect square trinomial form, we can write it as $(a-b)^2$.
Substituting $a=p$ and $b=3$:

The completely factored form of the expression is: