X2 + 16x + 64

A perfect square trinomial has the form $a^2 + 2ab + b^2 = (a+b)^2$.
In our expression, $x^2$ corresponds to $a^2$, so $a = x$.
The constant term 64 corresponds to $b^2$, so $b = \sqrt{64} = 8$.

The middle term of a perfect square trinomial should be $2ab$.
Using $a=x$ and $b=8$, we calculate $2ab = 2(x)(8) = 16x$.
This matches the middle term of the given expression, $16x$.

Since it fits the perfect square trinomial form, we can write it as $(a+b)^2$.
Substituting $a=x$ and $b=8$:

The completely factored form of the expression is: