Standard Identities

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

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

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

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

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

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

(7) $\begin{equation*} (a + b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac\end{equation*}$

(8) $\begin{equation*} a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)\end{equation*}$

if $a+b+c=0$ then

(9) $\begin{equation*} a^3+b^3+c^3=3abc\end{equation*}$

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

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

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

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

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

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

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

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