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Special factoring rules of polynomials


\begin{align}
  \displaystyle a^2 + 2ab+b^2 &=(a + b)^2 \tag{1}\\
  \displaystyle a^2 - 2ab+b^2 &=(a - b)^2 \tag{2}\\
  \displaystyle a^2-b^2 &=(a+b)(a-b) \tag{3}\\
  \displaystyle a^3 + 3a^2b+3ab^2 + b^3 &=(a + b)^3 \tag{4}\\
  \displaystyle a^3 - 3a^2b+3ab^2 - b^3 &=(a - b)^3 \tag{5}\\
  \displaystyle a^3 - b^3 &=(a - b)(a^2 + ab+b^2) \tag{6}\\
  \displaystyle a^3 + b^3 &=(a + b)(a^2 - ab+b^2) \tag{7}
\end{align}
(1) and (2) - perfect squares of trinomials, (3) - difference of squares, (4) and (5) - perfect cubes, (6) - difference of cubes, (7) - sum of cubes.

Last time edited 2019-01-19

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