因数 125d^6a^3+216t^3e^9

解

因数

125 d^{6} a^{3} + 216 t^{3} e^{9}

(5 d^{2} a + 6 e^{3} t) (25 d^{4} a^{2} - 30 e^{3} d^{2} a t + 36 e^{6} t^{2})

解答ステップ

125 d^{6} a^{3} + 216 t^{3} e^{9}

125 d^{6} a^{3}

を書き換え

(5 d^{2} a)^{3}

216 t^{3} e^{9}

を書き換え

(6 t e^{3})^{3}

= (5 d^{2} a)^{3} + (6 t e^{3})^{3}

立方数の和の公式を適用する:

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

(5 d^{2} a)^{3} + (6 t e^{3})^{3} = (5 d^{2} a + 6 t e^{3}) ((5 d^{2} a)^{2} - 5 d^{2} a 6 t e^{3} + (6 t e^{3})^{2})

= (5 d^{2} a + 6 t e^{3}) ((5 d^{2} a)^{2} - 5 d^{2} a 6 t e^{3} + (6 t e^{3})^{2})

簡素化

(5 d^{2} a + 6 t e^{3}) ((5 d^{2} a)^{2} - 5 d^{2} a \cdot 6 t e^{3} + (6 t e^{3})^{2}) : (5 d^{2} a + 6 e^{3} t) (25 d^{4} a^{2} - 30 e^{3} d^{2} a t + 36 e^{6} t^{2})

= (5 d^{2} a + 6 e^{3} t) (25 d^{4} a^{2} - 30 e^{3} d^{2} a t + 36 e^{6} t^{2})