Factor the first three terms and keep bringing the -4 down
to the next line:

a²-2ab+b² - 4
                 Factor the a²-2ab+b² first as (a-b)(a-b) 
                 and then shorten that to (a-b)² and bring down the - 4
                 to the next line, like this:

(a-b)² - 4


                 Now we recognize 4 as the square, 2², so we write 4 as 2²

(a-b)² - 2²
                 Now we recognize that as the difference of two squares
                 And we factor it this way using brackets to hold the
                 parentheses.  It's just like factoring x²-4 as (x-2)(x+2)
                 except you have a parentheses instead of x, and brackets
                 instead of parentheses:

[(a-b) - 2][(a-b) + 2]

Then you take out the parenthese inside 

[a - b - 2][a- b + 2]

and finally change the brackets to
parentheses:

(a - b - 2)(a - b + 2)

Edwin