因数 x^6-8x^6

解

因数

x^{6} - 8 x^{6}

- 7 x^{6}

解答ステップ

x^{6} - 8 x^{6}

8 x^{6}

を書き換え

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

= x^{6} - (2 x^{2})^{3}

指数の規則を適用する:

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

x^{6} = (x^{2})^{3}

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

= (x^{2} - 2 x^{2}) (x^{4} + x^{2} 2 x^{2} + (2 x^{2})^{2})

簡素化

(x^{2} - 2 x^{2}) (x^{4} + x^{2} \cdot 2 x^{2} + (2 x^{2})^{2}) : - 7 x^{6}

= - 7 x^{6}