展開する 2(x_{1}+x_{2}+x_{3})^2-x_{2}-x_{3}

解

展開する

2 (x_{1} + x_{2} + x_{3})^{2} - x_{2} - x_{3}

4 x_{1} x_{2} + 4 x_{1} x_{3} + 2 x_{1}^{2} + 2 x_{2}^{2} + 4 x_{2} x_{3} + 2 x_{3}^{2} - x_{2} - x_{3}

解答ステップ

2 (x_{1} + x_{2} + x_{3})^{2} - x_{2} - x_{3}

(x_{1} + x_{2} + x_{3})^{2} = 2 x_{1} x_{2} + 2 x_{1} x_{3} + x_{1}^{2} + x_{2}^{2} + 2 x_{2} x_{3} + x_{3}^{2}

= 2 (x_{1}^{2} + 2 x_{1} x_{2} + 2 x_{1} x_{3} + x_{2}^{2} + 2 x_{2} x_{3} + x_{3}^{2}) - x_{2} - x_{3}

拡張

2 (2 x_{1} x_{2} + 2 x_{1} x_{3} + x_{1}^{2} + x_{2}^{2} + 2 x_{2} x_{3} + x_{3}^{2}) : 4 x_{1} x_{2} + 4 x_{1} x_{3} + 2 x_{1}^{2} + 2 x_{2}^{2} + 4 x_{2} x_{3} + 2 x_{3}^{2}

= 4 x_{1} x_{2} + 4 x_{1} x_{3} + 2 x_{1}^{2} + 2 x_{2}^{2} + 4 x_{2} x_{3} + 2 x_{3}^{2} - x_{2} - x_{3}