因数 x^3y^6z^{12}-512

解

因数

x^{3} y^{6} z^{12} - 512

(x y^{2} z^{4} - 8) (x^{2} y^{4} z^{8} + 8 x y^{2} z^{4} + 64)

解答ステップ

x^{3} y^{6} z^{12} - 512

x^{3} y^{6} z^{12}

を書き換え

(x y^{2} z^{4})^{3}

= (x y^{2} z^{4})^{3} - 512

512

を書き換え

8^{3}

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

= (x y^{2} z^{4} - 8) ((x y^{2} z^{4})^{2} + 8 x y^{2} z^{4} + 8^{2})

改良

= (x y^{2} z^{4} - 8) ((x y^{2} z^{4})^{2} + 8 x y^{2} z^{4} + 64)

簡素化

(x y^{2} z^{4} - 8) ((x y^{2} z^{4})^{2} + 8 x y^{2} z^{4} + 64) : (x y^{2} z^{4} - 8) (x^{2} y^{4} z^{8} + 8 x y^{2} z^{4} + 64)

= (x y^{2} z^{4} - 8) (x^{2} y^{4} z^{8} + 8 x y^{2} z^{4} + 64)