Latex tip 207: Tips for using align environment to enter multi-line formulas

Align is the best use of the input multi-line formula in the environment, is only a personal humble opinion, because his alignment is very flexible, if we need a very smart alignment of the multi-line formula, it is recommended to use the Align environment, the corresponding also has align* and aligned and other similar environment, here no longer detailed. The following provides the code to show its graceful.
Demo:






Demo Code:
\documentclass{article}
\pagestyle{empty}
\SETCOUNTER{PAGE}{6}
\SETLENGTH\TEXTWIDTH{266.0PT}
\USEPACKAGE{CJK}
\usepackage{amsmath}

\begin{cjk}{gbk}{song}
\begin{document}

\begin{align}
(A + B) ^3 &= (A + B) (A + b) ^2 \ \
&= (A + B) (a^2 + 2ab + b^2) \ \
&= a^3 + 3a^2b + 3ab^2 + b^3
\end{align}
\begin{align}
X^2 + y^2 & = 1 \ \
X & = \sqrt{1-y^2}
\end{align}
This example has a column-pairs.
\begin{align} \text{compare}
x^2 + y^2 &= 1 &
X^3 + y^3 &= 1 \ \
X &= \sqrt {1-y^2} &
x &= \sqrt[3]{1-y^3}
\end{align}
This example has three column-pairs.
\begin{align}
X &= y & x &= y &
A &= b+c \ \
X ' &= y ' & x ' &= y ' &
A ' &= b \ \
x + x ' &= y + y ' &
x + x ' &= y + y ' & A ' B &= c ' b
\end{align}

This example has a column-pairs.
\begin{flalign} \text{compare}
x^2 + y^2 &= 1 &
X^3 + y^3 &= 1 \ \
X &= \sqrt {1-y^2} &
x &= \sqrt[3]{1-y^3}
\end{flalign}
This example has three column-pairs.
\begin{flalign}
X &= y & x &= y &
A &= b+c \ \
X ' &= y ' & x ' &= y ' &
A ' &= b \ \
x + x ' &= y + y ' &
x + x ' &= y + y ' & A ' B &= c ' b
\end{flalign}

This example has a column-pairs.
\RENEWCOMMAND\MINALIGNSEP{0PT}
\begin{align} \text{compare}
x^2 + y^2 &= 1 &
X^3 + y^3 &= 1 \ \
X &= \sqrt {1-y^2} &
x &= \sqrt[3]{1-y^3}
\end{align}
This example has three column-pairs.
\RENEWCOMMAND\MINALIGNSEP{15PT}
\begin{flalign}
X &= y & x &= y &
A &= b+c \ \
X ' &= y ' & x ' &= y ' &
A ' &= b \ \
x + x ' &= y + y ' &
x + x ' &= y + y ' & A ' B &= c ' b
\end{flalign}

\RENEWCOMMAND\MINALIGNSEP{2EM}
\begin{align}
X &= y && \text{by hypothesis} \ \
X ' &= y ' && \text{by definition} \ \
x + x ' &= y + y ' && \text{by Axiom 1}
\end{align}

\begin{equation}
\begin{aligned}
x^2 + y^2 &= 1 \ \
x &= \sqrt{1-y^2} \ \
\text{and also}y &= \sqrt{1-x^2}
\end{aligned} \qquad
\begin{gathered}
(A + b) ^2 = a^2 + 2ab + b^2 \ \
(A + B) \cdot (a) = A^2-b^2
\end{gathered} \end{equation}

\begin{equation}
\BEGIN{ALIGNED}[B]
x^2 + y^2 &= 1 \ \
x &= \sqrt{1-y^2} \ \
\text{and also}y &= \sqrt{1-x^2}
\end{aligned} \qquad
\BEGIN{GATHERED}[T]
(A + b) ^2 = a^2 + 2ab + b^2 \ \
(A + B) \cdot (a) = A^2-b^2
\end{gathered}
\end{equation}
\newenvironment{rcase}
{\left.\begin{aligned}}
{\end{aligned}\right\rbrace}

\begin{equation*}
\begin{rcase}
B ' &=-\partial\times E \ \
E ' &= \partial\times b-4\pi j \,
\end{rcase}
\quad \text {Maxwell ' s equations}
\end{equation*}

\begin{equation} \begin{aligned}
V_j &= V_j &
X_i &= x_i-q_i X_j &
&= U_j + \sum_{i\ne J} q_i \ \
V_i &= v_i-q_i V_j &
X_j &= X_j &
U_i &= u_i
\end{aligned} \end{equation}

\begin{align}
A_1 &= n_0 (\lambda; \omega ')
-\phi (\LAMBDA; \omega ') \ \
a_2 &= \phi (\lambda; \omega ')
\phi (\LAMBDA; \omega) \ \
\intertext{and finally}
A_3 &= \mathcal{n} (\LAMBDA; \omega)
\end{align}
\END{CJK}
\end{document}

From:http://blog.sina.com.cn/s/blog_5e16f1770100gror.html

Latex tip 207: Tips for using align environment to enter multi-line formulas