因数 125x^9y^{18}-512z^{27}

解

因数

125 x^{9} y^{18} - 512 z^{27}

(5 x^{3} y^{6} - 8 z^{9}) (25 x^{6} y^{12} + 40 x^{3} y^{6} z^{9} + 64 z^{18})

解答ステップ

125 x^{9} y^{18} - 512 z^{27}

125 x^{9} y^{18}

を書き換え

(5 x^{3} y^{6})^{3}

512 z^{27}

を書き換え

(2 z^{3})^{9}

= (5 x^{3} y^{6})^{3} - (2 z^{3})^{9}

指数の規則を適用する:

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

(2 z^{3})^{9} = ((2 z^{3})^{3})^{3}

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

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

簡素化

(5 x^{3} y^{6} - (2 z^{3})^{3}) ((5 x^{3} y^{6})^{2} + (2 z^{3})^{3} \cdot 5 x^{3} y^{6} + (2 z^{3})^{6}) : (5 x^{3} y^{6} - 8 z^{9}) (25 x^{6} y^{12} + 40 x^{3} y^{6} z^{9} + 64 z^{18})

= (5 x^{3} y^{6} - 8 z^{9}) (25 x^{6} y^{12} + 40 x^{3} y^{6} z^{9} + 64 z^{18})