# How to put equations and equivalence in Latex

I am trying to put the following equation and equivalence in Latex, but I face with strange output, May you please help me to solve this issue:

\begin{document}
\begin{flalign*}
(f_{uvw},f_{u_{1}v_{1}w_{1}})_{[u]([v][w])} & =f_{uvw}-f_{u_{1}v_{1}w_{1}} &\\
&= [u]([v]([v_{1}][w_{1}]))-([u][v])([v_{1}][w_{1}])+([u]([v_{1}][w_{1}]))[v]\\
&-[u]([v]([v_{1}][w_{1}]))+[u](([v][v_{1}])[w_{1}])-[u](([v][w_{1}])[v_{1}])&\\
\equiv -(([u][v])[v_{1}])[w_{1}] + (([u][v])[w_{1}])[v_{1}] +(([u][v_{1}])[w_{1}])[v_{1}] \\
& -(([u][w_{1}])[v_{1}])[v] + (([u][v])[v_{1}])[w_{1}] -(([u][v_{1}])[v])[w_{1}] \\
&-(([u][w_{1}])[v])[v_{1}] + (([u][w_{1}])[v_{1}])[v]-(([u][v])[w_{1}])[v_{1}]  \\
&+(([u][w_{1}])[v])[v_{1}] +(([u][v_{1}])[v])[w_{1}] _(([u][v_{1}])[w_{1}])[v_{1}]
\end{flalign*}
\end{document}

• Welcome to TeX.SX! I'm not sure you really need flalign; I find it's often a bit abused. Apr 1, 2017 at 16:40

You don't say what output you want but I guess you are missing one & \documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{flalign*}
(f_{uvw},f_{u_{1}v_{1}w_{1}})_{[u]([v][w])} & =f_{uvw}-f_{u_{1}v_{1}w_{1}} &\\
&= [u]([v]([v_{1}][w_{1}]))-([u][v])([v_{1}][w_{1}])+([u]([v_{1}][w_{1}]))[v]\\
&-[u]([v]([v_{1}][w_{1}]))+[u](([v][v_{1}])[w_{1}])-[u](([v][w_{1}])[v_{1}])&\\
\equiv
&
-(([u][v])[v_{1}])[w_{1}] + (([u][v])[w_{1}])[v_{1}] +(([u][v_{1}])[w_{1}])[v_{1}] \\
& -(([u][w_{1}])[v_{1}])[v] + (([u][v])[v_{1}])[w_{1}] -(([u][v_{1}])[v])[w_{1}] \\
&-(([u][w_{1}])[v])[v_{1}] + (([u][w_{1}])[v_{1}])[v]-(([u][v])[w_{1}])[v_{1}]  \\
&+(([u][w_{1}])[v])[v_{1}] +(([u][v_{1}])[v])[w_{1}] _(([u][v_{1}])[w_{1}])[v_{1}]
\end{flalign*}
\end{document}


Just for fun [!?], here's a refinement of David's approach. It adds a bit of extra vertical whitespace after rows 1 and 3, it provides indentation of the material in rows 3, 5, 6, and 7, and it fixes an issue with the material that's supposed to be in subscript in the final additive term in the final row. \documentclass{article}
\usepackage{amsmath} % for 'flalign*' env.
\begin{document}
\begin{flalign*}
(f_{uvw},f_{u_1 v_1 w_1})_{[u]([v][w])}
&= f_{uvw}-f_{u_1v_1w_1} \\[0.5ex]
&=      [u]([v]([v_1][w_1]))-([u][v])([v_1][w_1])+([u]([v_1][w_1]))[v]\\
&\equiv-(([u][v])[v_1])[w_1] + (([u][v])[w_1])[v_1] +(([u][v_1])[w_1])[v_1] \\
&\quad -(([u][w_1])[v_1])[v] + (([u][v])[v_1])[w_1] -(([u][v_1])[v])[w_1] \\
&\quad -(([u][w_1])[v])[v_1] + (([u][w_1])[v_1])[v] -(([u][v])[w_1])[v_1]  \\
\end{flalign*}
\end{document}


Some more fun with fleqn from nccmath and multlined from mathtools. I interpreted differently the code at the end of the last line:

\documentclass{article}
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.3pt}
\usepackage{mathtools, nccmath}

\begin{document}

\begin{fleqn}
\begin{align*}
& \mathrlap{ (f_{uvw},f_{u_{1}v_{1}w_{1}})_{[u]([v][w])} =f_{uvw}-f_{u_{1}v_{1}w_{1}}} \\
& & & =\begin{multlined}[t] [u]([v]([v_{1}][w_{1}]))-([u][v])([v_{1}][w_{1}])+([u]([v_{1}][w_{1}]))[v]\\
-[u]([v]([v_{1}][w_{1}]))+[u](([v][v_{1}])[w_{1}])-[u](([v][w_{1}])[v_{1}])\end{multlined}\\
& & & \equiv
\begin{multlined}[t]
-(([u][v])[v_{1}])[w_{1}] + (([u][v])[w_{1}])[v_{1}] +(([u][v_{1}])[w_{1}])[v_{1}] \\
-(([u][w_{1}])[v_{1}])[v] + (([u][v])[v_{1}])[w_{1}] -(([u][v_{1}])[v])[w_{1}] \\
-(([u][w_{1}])[v])[v_{1}] + (([u][w_{1}])[v_{1}])[v]-(([u][v])[w_{1}])[v_{1}] \\
+(([u][w_{1}])[v])[v_{1}] +(([u][v_{1}])[v])[w_{1}]-(([u][v_{1}])[w_{1}])[v_{1}]
\end{multlined}
\end{align*}
\end{fleqn}

\end{document} • +1. I see you interpreted the _ (underscore) character in the last line as a typo and replaced it with -. Was this a hunch or did you actually understand the mathematics sufficiently to realize that _ was a typo? Just curious.
– Mico
Apr 2, 2017 at 7:07