Clear["Global`*"]
In[]:=
-1+2Subscript[λ,1]^2Subscript[λ,2]^4-Subscript[λ,1]^4Subscript[λ,2]^8/.{1-2Subscript[λ,1]^2Subscript[λ,2]^4+Subscript[λ,1]^4Subscript[λ,2]^8Subscript[δ,2]}​​Quit
Out[]=
-1+2
2
λ
1
4
λ
2
-
4
λ
1
8
λ
2