乗法の公式 (x+3)^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