U can use this middle term splitting in a quadratic eqaution for example to spit middle ternm in a way that there is common of one set in both sides 
2 3 2
In a quadratic equation, the middle term should be splitted in such a way that the product of 1st and the 3rd term is equal to the two parts of the middle term.
Ex: 3x^2+10x-25=0
The middle term should be split such that the product of two parts equal (-25*3)=-75
Therefore, the two parts should be +15x and -5x as their sum is +10x and their product is -75.
1 4 1
The equation after splitting the 2nd term would be: x^2+4x-2x-8
therefore, x=2 or -4
4s^2-4s+1= 4s^2-2s-2s+1
thank u Ruhani
Your'e welcome :)