因数 d^3e^6f^9-216

解

因数

d^{3} e^{6} f^{9} - 216

(e^{2} d f^{3} - 6) (e^{4} d^{2} f^{6} + 6 e^{2} d f^{3} + 36)

解答ステップ

d^{3} e^{6} f^{9} - 216

d^{3} e^{6} f^{9}

を書き換え

(d e^{2} f^{3})^{3}

= (d e^{2} f^{3})^{3} - 216

216

を書き換え

6^{3}

= (d e^{2} f^{3})^{3} - 6^{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})

(d e^{2} f^{3})^{3} - 6^{3} = (d e^{2} f^{3} - 6) ((d e^{2} f^{3})^{2} + 6 d e^{2} f^{3} + 6^{2})

= (d e^{2} f^{3} - 6) ((d e^{2} f^{3})^{2} + 6 d e^{2} f^{3} + 6^{2})

改良

= (d e^{2} f^{3} - 6) ((d e^{2} f^{3})^{2} + 6 d e^{2} f^{3} + 36)

簡素化

(d e^{2} f^{3} - 6) ((d e^{2} f^{3})^{2} + 6 d e^{2} f^{3} + 36) : (e^{2} d f^{3} - 6) (e^{4} d^{2} f^{6} + 6 e^{2} d f^{3} + 36)

= (e^{2} d f^{3} - 6) (e^{4} d^{2} f^{6} + 6 e^{2} d f^{3} + 36)