因数 8x^{18}-729y^3z^{15}

解

因数

8 x^{18} - 729 y^{3} z^{15}

(2 x^{6} - 9 y z^{5}) (4 x^{12} + 18 x^{6} y z^{5} + 81 y^{2} z^{10})

解答ステップ

8 x^{18} - 729 y^{3} z^{15}

8 x^{18}

を書き換え

(2 x^{6})^{3}

729 y^{3} z^{15}

を書き換え

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

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

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

簡素化

(2 x^{6} - 3^{2} y z^{5}) ((2 x^{6})^{2} + 2 x^{6} \cdot 3^{2} y z^{5} + (3^{2} y z^{5})^{2}) : (2 x^{6} - 9 y z^{5}) (4 x^{12} + 18 x^{6} y z^{5} + 81 y^{2} z^{10})

= (2 x^{6} - 9 y z^{5}) (4 x^{12} + 18 x^{6} y z^{5} + 81 y^{2} z^{10})