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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