Answer
$z^2-12z+36=(x-6)^2$
Work Step by Step
We add the square of half of the coefficent of $z$ so that the result is a perfect square trinomial.
Co-efficient of $z=-12$
Half of -12 is $\frac{1}{2}×-12=-6$
Square of -6 is $-6×-6=36$
We add 36 to $z^2-12z$ to make it a perfect square trinomial.
Hence it becomes $z^2-12z+36$
Factored form-
$z^2-12z+36$
$=z^2-6z-6z+36$
$=z(z-6)-6(z-6)$ (Taking the common factors)
$=(z-6)(z-6)$ ($ z-6$ is taken common from both the terms)
$=(z-6)^2$
