因数 x^3y^6z^{12}-t^{12}

解

因数

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

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

解答ステップ

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

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

を書き換え

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

= (x y^{2} z^{4})^{3} - t^{12}

指数の規則を適用する:

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

t^{12} = (t^{4})^{3}

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

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

簡素化

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

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