Answer
$(x-6+a)(x-6-a)$
Work Step by Step
Grouping the first $3$ terms the given expression is equivalent to
\begin{array}{l}\require{cancel}
36-12x+x^2-a^2
\\\\=
(36-12x+x^2)-a^2
\\\\=
(x^2-12x+36)-a^2
.\end{array}
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
(x^2-12x+36)
\end{array} has $c=
36
$ and $b=
-12
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-6,-6
\right\}.$ Using these two numbers, the $\text{
expression
}$ above is equivalent to
\begin{array}{l}\require{cancel}
(x-6)(x-6)-a^2
\\\\=
(x-6)^2-a^2
.\end{array}
The expressions $
(x-6)^2
$ and $
a^2
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
(x-6)^2-a^2
,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(x-6)^2-(a)^2
\\\\=
(x-6+a)(x-6-a)
.\end{array}
