因数 x^9-125y^3z^6

解

因数

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

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

解答ステップ

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

125 y^{3} z^{6}

を書き換え

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

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

指数の規則を適用する:

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

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

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

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

簡素化

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

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