There is no need to change signs in Mid - Term Splitting !! You just need to put the sign after the second term.
Here is an example
8x² - 2x -2
splitting the middle term
8x² - 4x + 2x - 2
If I am not wrong you are confused in determining the signs of the terms that you write in the place of the middle term
In th eg
If I take 4x - 2x 
I would get +2x
not needed as the middle term is -2x
If I take -4x -2x we would get -6x     not needed
If  I take 4x + 2x we would get 6x     not needed
But when i take -4x +2x we get -2x
That is what we exactly need!
Therefore I write as
8x² - 4x +2x -2.
I hope this answer will help you out and drag you out of confusion
To really understand please read it patiently..