因数 8x^9-125y^6z^9

解

因数

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

(2 x^{3} - 5 y^{2} z^{3}) (4 x^{6} + 10 x^{3} y^{2} z^{3} + 25 y^{4} z^{6})

解答ステップ

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

8 x^{9}

を書き換え

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

125 y^{6} z^{9}

を書き換え

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

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

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

簡素化

(2 x^{3} - 5 y^{2} z^{3}) ((2 x^{3})^{2} + 2 x^{3} \cdot 5 y^{2} z^{3} + (5 y^{2} z^{3})^{2}) : (2 x^{3} - 5 y^{2} z^{3}) (4 x^{6} + 10 x^{3} y^{2} z^{3} + 25 y^{4} z^{6})

= (2 x^{3} - 5 y^{2} z^{3}) (4 x^{6} + 10 x^{3} y^{2} z^{3} + 25 y^{4} z^{6})