I will quote the following passage from Evans' book- pg 315:
Insert $v=(-1)^{|\alpha|}D^{\alpha}\tilde{v}$ into the identity $B[u,v]=(f,v)_{L^2(U)}$. After performing some integrations by parts, we get $$B[\tilde{u},\tilde{v}]=(\tilde{f},\tilde{v})$$ where $\tilde{u}=D^{\alpha}u$ and $\tilde{f}=D^{\alpha}f-\sum{a\choose b}[-\sum\dots]$
I haven't completed the terms in the brackets. According to my calculations, $\tilde{f}$ should only be equal to $D^{\alpha} f$. Where did the rest of the terms come from?