展開・因数分解の公式

\( (a \pm b)^2 = a^2 \pm 2ab \pm b^2 \)
\( (a + b)(a – b) = a^2 – b^2 \)
\( (ax + b)(cx + d) = acx^2 + (ad + bc)x + bd \)
\( (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \) (複号同順)
\( (a \pm b)^3 = a^3 \pm 3a^2b + 3ab^2 \pm b^3 \) (複号同順)
\( (a + b + c)(a^2 + b^2 + c^2 – ab – bc – ca) = \displaystyle \frac{1}{2} (a + b + c)\{(a – b)^2 + (b – c)^2 + (c – a)^2\} = a^3 + b^3 + c^3 -3abc \)