因数 8p^3-d^3e^3

解

因数

8 p^{3} - d^{3} e^{3}

(2 p - e d) (4 p^{2} + 2 e p d + e^{2} d^{2})

解答ステップ

8 p^{3} - d^{3} e^{3}

8 p^{3}

を書き換え

(2 p)^{3}

d^{3} e^{3}

を書き換え

(d e)^{3}

= (2 p)^{3} - (d e)^{3}

立方数の差の公式を適用する:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(2 p)^{3} - (d e)^{3} = (2 p - d e) ((2 p)^{2} + 2 p d e + (d e)^{2})

= (2 p - d e) ((2 p)^{2} + 2 p d e + (d e)^{2})

簡素化

(2 p - d e) ((2 p)^{2} + 2 p d e + (d e)^{2}) : (2 p - e d) (4 p^{2} + 2 e p d + e^{2} d^{2})

= (2 p - e d) (4 p^{2} + 2 e p d + e^{2} d^{2})