Before insert dielectric, capacitance, C0=Aϵ0d
Magnitude of charge on each plate, Q=C0V=Aϵ0dV
Before disconnect the battery, filed between the plates, E0=Vd
Afe insert dielectric, electric filed, E=E0K=VKd
Before insert dielectric, work done, =Wi=12C0V2
After insert work done, Wf=12(KC0)(VK)2. (Cf=Aϵ0Kd,Vf=Ed)
So net work done,W=Wi−Wf=12C0V2−12(KC0)(VK)2=12C0V2(1−1K)=Aϵ0V2d(1−1K)