If α and β are the zeros of the polynomial $f\left(x\right)=x^2-5x+k \mathrm{such} \mathrm{that} \mathrm{\alpha }-\mathrm{\beta }=1$, find the value of k.

Check the previous step.
It says (a-b)^2.
It is the same as saying: (a+b)^2-4ab
Because if you expand it, you will be getting (a-b)^2 again. Hence, there's no disturbance in the equation.
It's done to get the value of (a-b).
Hope you understand. If you have any doubt, please reply and I'll try to help.
Hope that helps.
Cheers!