乗法の公式 (x-y)^3

${\displaystyle {\left(x-y\right)}^3}$ 

${\displaystyle =\left(x-y\right)\left(x-y\right)\left(x-y\right)}$ 

${\displaystyle =\left\{x\left(x-y\right)-y\left(x-y\right)\right\}\left(x-y\right)}$ 

${\displaystyle =\left(x^2-xy-yx+y^2\right)\left(x-y\right)}$

${\displaystyle =\left(x^2-xy-xy+y^2\right)\left(x-y\right)}$

${\displaystyle =\left(x^2-2xy+y^2\right)\left(x-y\right)}$ 

${\displaystyle =\left(x-y\right)\left(x^2-2xy+y^2\right)}$

${\displaystyle =x\left(x^2-2xy+y^2\right)-y\left(x^2-2xy+y^2\right)}$

${\displaystyle =x^3-2x^{2}y+x{y}^2-y{x}^2+2x{y}^2-y^3}$

${\displaystyle =x^3-2x^{2}y+x{y}^2-x^{2}y+2x{y}^2-y^3}$

${\displaystyle =x^3-3x^{2}y+3x{y}^2-y^3}$ ⇒ 参照

　

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最終更新日： 2023年7月12日