Steps to factor the polynomial

Question

Please provide detailed steps on how to factor the following polynomial

 

12m²n² - 8mn + 1

Answer 1

This is a trinomial in  mn.   To make it look more familiar ,  let  x = mn   then

 

12 x² - 8 x + 1       this is not difficult to factor  - it is just

 

(6 x -1) (2 x -1)

 

putting back mn  for x   we get

 

( 6 mn -1) (2 mn -1)