因数 125x^3y^6z^{12}-d^9

解

因数

125 x^{3} y^{6} z^{12} - d^{9}

(5 x y^{2} z^{4} - d^{3}) (25 x^{2} y^{4} z^{8} + 5 d^{3} x y^{2} z^{4} + d^{6})

解答ステップ

125 x^{3} y^{6} z^{12} - d^{9}

125 x^{3} y^{6} z^{12}

を書き換え

(5 x y^{2} z^{4})^{3}

= (5 x y^{2} z^{4})^{3} - d^{9}

指数の規則を適用する:

a^{b c} = (a^{b})^{c}

d^{9} = (d^{3})^{3}

= (5 x y^{2} z^{4})^{3} - (d^{3})^{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})

(5 x y^{2} z^{4})^{3} - (d^{3})^{3} = (5 x y^{2} z^{4} - d^{3}) ((5 x y^{2} z^{4})^{2} + 5 x y^{2} z^{4} d^{3} + d^{6})

= (5 x y^{2} z^{4} - d^{3}) ((5 x y^{2} z^{4})^{2} + 5 x y^{2} z^{4} d^{3} + d^{6})

簡素化

(5 x y^{2} z^{4} - d^{3}) ((5 x y^{2} z^{4})^{2} + 5 x y^{2} z^{4} d^{3} + d^{6}) : (5 x y^{2} z^{4} - d^{3}) (25 x^{2} y^{4} z^{8} + 5 d^{3} x y^{2} z^{4} + d^{6})

= (5 x y^{2} z^{4} - d^{3}) (25 x^{2} y^{4} z^{8} + 5 d^{3} x y^{2} z^{4} + d^{6})