\begin{equation*} a^2 - b^2 = (a + b)(a-b) \end{equation*}

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

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

\begin{equation*} a^2+2ab+b^2=(a+b)^2 \end{equation*}

\begin{equation*} a^2-2ab+b^2=(a-b)^2 \end{equation*}

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

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

\begin{equation*} a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b+…-ab^{n-2}+b^{n-1}) , n为正奇数 \end{equation*}

\begin{equation*} a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b+…+ab^{n-2}+b^{n-1}), n为正整数 \end{equation*}

\begin{equation*} a^3+b^3+c^3-3abc=\frac{1}{2}(a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]，由轮换式可推 \end{equation*}