因数 x^6y^9-125z^{12}

解

因数

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

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

解答ステップ

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

x^{6} y^{9}

を書き換え

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

125 z^{12}

を書き換え

(5 z^{4})^{3}

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

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

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

簡素化

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

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