\documentclass{amsart}

\newcommand{\pathtotrunk}{../../}
\input{\pathtotrunk text/article_preamble.tex}

\pagestyle{empty}

\begin{document}
\thispagestyle{empty}

\newcommand{\tm}{\widetilde{m}}
\newcommand{\ttm}{\widetilde{\widetilde{m}}}

\begin{align*}
\bdy(\tm_4(a \tensor b \tensor c \tensor d)) & = (\tm_4(\bdy a \tensor b \tensor c \tensor d) + \cdots + \tm_4(a \tensor b \tensor c \tensor \bdy d)) + \\
                                             & + (\tm_3(a \tensor b \tensor c) \tensor d + \tm_2(a \tensor b) \tensor \tm_2(c \tensor d) + a \tensor \tm_3(b \tensor c \tensor d)) + \\
                                             & + (\tm_3(m_2(a \tensor b) \tensor c \tensor d) + \tm_3(a \tensor m_2(b \tensor c) \tensor d) + \tm_3(a \tensor b \tensor m_2(c \tensor d)) + \\
                                             & + \tm_2(m_3(a \tensor b \tensor c) \tensor d) + \tm_2(a \tensor m_3(b \tensor c \tensor d)) + m_4(a \tensor b \tensor c \tensor d)) \\
\end{align*}
\end{document}