簡約 2pi^2(-x^2+2e)^2*(-12 3/4+y^2+2/8)^2

解

簡約

2 π^{2} (- x^{2} + 2 e)^{2} \cdot (- 12 \frac{3}{4} + y^{2} + \frac{2}{8})^{2}

2 π^{2} (x^{4} y^{4} + \frac{625 x ^{4}}{4} - 25 x^{4} y^{2} + 100 e x^{2} y^{2} - 625 e x^{2} - 4 e x^{2} y^{4} + 4 e^{2} y^{4} + 625 e^{2} - 100 e^{2} y^{2})

解答ステップ

2 π^{2} (- x^{2} + 2 e)^{2} \cdot (- 12 \frac{3}{4} + y^{2} + \frac{2}{8})^{2}

帯分数を仮分数に変換する:

12 \frac{3}{4} = \frac{51}{4}

= 2 π^{2} (- x^{2} + 2 e)^{2} \cdot (- \frac{51}{4} + y^{2} + \frac{2}{8})^{2}

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m},

, 以下を想定

a \geq 0, b \geq 0

(- x^{2} + 2 e)^{2} (y^{2} + \frac{2}{8} - \frac{51}{4})^{2} = ((- x^{2} + 2 e) (y^{2} + \frac{2}{8} - \frac{51}{4}))^{2}

= 2 π^{2} ((- x^{2} + 2 e) (y^{2} + \frac{2}{8} - \frac{51}{4}))^{2}

簡素化

(- x^{2} + 2 e) (- \frac{51}{4} + y^{2} + \frac{2}{8}) : - x^{2} y^{2} + \frac{25 x ^{2}}{2} + 2 e y^{2} - 25 e

= 2 π^{2} (\frac{25 x ^{2}}{2} - x^{2} y^{2} + 2 e y^{2} - 25 e)^{2}

(- x^{2} y^{2} + \frac{25 x ^{2}}{2} + 2 e y^{2} - 25 e)^{2} = - 625 e x^{2} + x^{4} y^{4} - 25 x^{4} y^{2} - 4 e x^{2} y^{4} + 100 e x^{2} y^{2} + \frac{625 x ^{4}}{4} + 625 e^{2} + 4 e^{2} y^{4} - 100 e^{2} y^{2}

= 2 π^{2} (x^{4} y^{4} + \frac{625 x ^{4}}{4} - 25 x^{4} y^{2} + 100 e x^{2} y^{2} - 625 e x^{2} - 4 e x^{2} y^{4} + 4 e^{2} y^{4} + 625 e^{2} - 100 e^{2} y^{2})