Align long equations

Question

I want to type the following equations by aligning them through the equal sign, but it seems to be too long:

\begin{align*}\prod_{z^n=-1}(w_1(z)^n+1)
&=& \prod_{l=0}^{l_0}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\times\prod_{l=l_1+1}^{n-1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\\
&=& \prod_{l=0}^{l_0}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^{-n}+1)\times\prod_{l=l_1+1}^{n-1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n)
\end{align*}

Someone can help me? Thanks a lot!

Answer 1

Just another way:

\documentclass[preview,border=12pt]{standalone}
\usepackage{mathtools}
\begin{document}
\abovedisplayskip=0pt\relax
\begin{align*}
\prod_{z^n=-1}(w_1(z)^n+1)
&=\!
    \begin{aligned}[t]
        &\prod_{l=0}^{l_0}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)
        \prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1) \\
        &\rule{10cm}{0pt}\mathllap{\times\prod_{l=l_1+1}^{n-1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)}
    \end{aligned} \\
&=\!
    \begin{aligned}[t]
        &\prod_{l=0}^{l_0}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)
        \prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^{-n}+1) \\
        &\rule{10cm}{0pt}\mathllap{\times\prod_{l=l_1+1}^{n-1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)
        \prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n)}
    \end{aligned}
\end{align*}
\end{document}

Note: \! is needed before aligned because of the issue discussed in Why is there a \, space at the beginning of the “aligned” environment?.

Answer 2

You could use the multlined environment from the mathtools package.

\documentclass[11pt]{article}
\usepackage{mathtools}
\begin{document}
\begin{align*}\prod_{z^n=-1}(w_1(z)^n+1)&=
\begin{multlined}[t]
 \prod_{l=0}^{l_0}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)
 \prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1) \\       \times\prod_{l=l_1+1}^{n-1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)
\end{multlined} \\    &=
\begin{multlined}[t]
  \prod_{l=0}^{l_0}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)
  \prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^{-n}+1) \\         \times\prod_{l=l_1+1}^{n-1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)    
     \prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n)
\end{multlined}
\end{align*}
\end{document}

You may want to change the location of the line breaks, depending on your font size, page width, etc.

Answer 3

If it is too long you have to split the line in two pieces

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\prod_{z^n=-1}(w_1(z)^n+1) &= \prod_{l=0}^{l_0}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\times\\
&\qquad\times\prod_{l=l_1+1}^{n-1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\\
&= \prod_{l=0}^{l_0}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^{-n}+1)\times\\
&\qquad\times\prod_{l=l_1+1}^{n-1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n+1)\prod_{l=l_0+1}^{l_1}(w_1(e^{\frac{(2l+1)\pi i}{n}})^n)
\end{align*}
\end{document}