(x2)2 + 182

That would be a perfect square if the term that is
twice the product of the square roots of those two
terms were added.  That's 2·18·x2 or 36x2.

So we add that between those terms and then subtract it.
That's the same as adding 0:

(x2)2 + 36x2 + 182 - 36x2

Factor the first three terms as (x2 + 18)(x2 + 18) or (x2 + 18)2

(x2 + 18)2 - 36x2

That is the difference of two perfect squares:

[(x2 + 18) - 6x][(x2 + 18) + 6x]

[x2 + 18 - 6x][x2 + 18 + 6x]

(x2 - 6x + 18)(x2 + 6x + 18)

Edwin