Aligned equations in LaTeX

\begin{aligned} (a+b)^2 &= (a+b)(a+b) \\ &= a^2 + 2ab + b^2 \end{aligned}

aligned works inside $$ ... $$ or \[ ... \] and keeps the whole block in one display. Put the & just before each equals sign so the rows line up there.

\begin{align}
  F &= ma \label{eq:newton} \\
  E &= mc^2 \nonumber
\end{align}

align numbers each row. \nonumber or \notag removes the number from one row, and a \label belongs on its own row, before the \\ that ends it.

\begin{aligned} x &= 1, & y &= 2 \\ z &= 3, & w &= 4 \end{aligned}

Every second & starts a new column: the first of each pair aligns, the next one separates columns. It is a compact way to list several short results.

\begin{aligned} f(x) &= a_0 + a_1 x + a_2 x^2 \\ &\quad + a_3 x^3 + a_4 x^4 \end{aligned}

When one equation is too wide for the page, break it before a plus or minus sign and indent the continuation with \quad after the &.

\begin{equation}
  \begin{split}
    (a+b)^3 &= (a+b)(a+b)^2 \\
            &= a^3 + 3a^2 b + 3ab^2 + b^3
  \end{split}
\end{equation}

split inside equation gives a multi-line derivation a single number, centred vertically. Use it when the steps lead to one result you cite once.