We need to prove this expression: $D[ξη]=DξDη+(Eξ)^2Dη+(Eη)^2Dξ$
I found a similar question where a person is trying to prove, but didn't get a couple of points. Do not think that I am asking again what is already on the site.
Proof:
$\begin{align}D[ξη] &=Eξ^2η^2−(Eξη)^2 \\&=Eξ^2Eη^2−(Eξ)^2(Eη)^2+(Eξ)^2Eη^2−(Eξη)^2 \\&=Eη^2(Eξ^2−(Eξ)^2)+Eξ^2(Eη^2−(Eη)^2) \\&=Eη^2Dξ+Eξ^2Dη \\&=DηDξ+(Eη)^2Dξ + (Eξ)^2Dη\end{align}$
Until this moment $D[ξη]=Eξ^2η^2−(Eξη)^2=Eξ^2Eη^2−(Eξ)^2(Eη)^2$, I perfectly understood everything, but why these two expressions $+(Eξ)^2Eη^2−(Eξη)^2$ appeared further on, I did not understand. Also, the moment remained unclear how from this $Eη^2Dξ$ he got this $Eη^2Dξ=DηDξ+(Eη)^2Dξ$ . Can you explain,please!