Factoring 12m^2n^2-8mn+1

12m^2n^2+8mn+1.

A*C = 12*1 = 12 = 1*12 = 2*6.
Select the pair of factors whose sum=B=8
(6,and 2).
12m^2n^2 + (2mn+6mn) +1.
Arrange the 4 terms into 2 factorable pairs:

(12m^2n^2+6mn) + (2mn+1)
6mn(2mn+1) + 1(2mn+1)
(2mn+1)(6mn+1)