展開する (e^2-2ey+y^2)(e^2-2x+x^2)-(e^2-2x+x^2)r

解

展開する

(e^{2} - 2 ey + y^{2}) (e^{2} - 2 x + x^{2}) - (e^{2} - 2 x + x^{2}) r

e^{4} - 2 e^{2} x + e^{2} x^{2} - 2 e^{3} y + 4 ey x - 2 ey x^{2} + e^{2} y^{2} - 2 y^{2} x + y^{2} x^{2} - e^{2} r + 2 x r - x^{2} r

解答ステップ

(e^{2} - 2 ey + y^{2}) (e^{2} - 2 x + x^{2}) - (e^{2} - 2 x + x^{2}) r

= (e^{2} - 2 ey + y^{2}) (e^{2} - 2 x + x^{2}) - r (e^{2} - 2 x + x^{2})

拡張

(e^{2} - 2 ey + y^{2}) (e^{2} - 2 x + x^{2}) : e^{4} - 2 e^{2} x + e^{2} x^{2} - 2 e^{3} y + 4 ey x - 2 ey x^{2} + e^{2} y^{2} - 2 y^{2} x + y^{2} x^{2}

= e^{4} - 2 e^{2} x + e^{2} x^{2} - 2 e^{3} y + 4 ey x - 2 ey x^{2} + e^{2} y^{2} - 2 y^{2} x + y^{2} x^{2} - (e^{2} - 2 x + x^{2}) r

拡張

- r (e^{2} - 2 x + x^{2}) : - e^{2} r + 2 x r - x^{2} r

= e^{4} - 2 e^{2} x + e^{2} x^{2} - 2 e^{3} y + 4 ey x - 2 ey x^{2} + e^{2} y^{2} - 2 y^{2} x + y^{2} x^{2} - e^{2} r + 2 x r - x^{2} r