因数 512x^6-27y^3z^9

解

因数

512 x^{6} - 27 y^{3} z^{9}

(8 x^{2} - 3 y z^{3}) (64 x^{4} + 24 x^{2} y z^{3} + 9 y^{2} z^{6})

解答ステップ

512 x^{6} - 27 y^{3} z^{9}

512 x^{6}

を書き換え

(2^{3} x^{2})^{3}

27 y^{3} z^{9}

を書き換え

(3 y z^{3})^{3}

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

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

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

簡素化

(2^{3} x^{2} - 3 y z^{3}) ((2^{3} x^{2})^{2} + 2^{3} x^{2} \cdot 3 y z^{3} + (3 y z^{3})^{2}) : (8 x^{2} - 3 y z^{3}) (64 x^{4} + 24 x^{2} y z^{3} + 9 y^{2} z^{6})

= (8 x^{2} - 3 y z^{3}) (64 x^{4} + 24 x^{2} y z^{3} + 9 y^{2} z^{6})