因数 1000x^6y^{12}-1

解

因数

1000 x^{6} y^{12} - 1

(10 x^{2} y^{4} - 1) (100 x^{4} y^{8} + 10 x^{2} y^{4} + 1)

解答ステップ

1000 x^{6} y^{12} - 1

指数の規則を適用する

= (10 x^{2} y^{4})^{3} - 1^{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})

(10 x^{2} y^{4})^{3} - 1^{3} = (10 x^{2} y^{4} - 1) ((10 x^{2} y^{4})^{2} + 10 x^{2} y^{4} + 1^{2})

= (10 x^{2} y^{4} - 1) ((10 x^{2} y^{4})^{2} + 10 x^{2} y^{4} + 1^{2})

簡素化

(10 x^{2} y^{4})^{2} + 10 x^{2} y^{4} + 1^{2} : 100 x^{4} y^{8} + 10 x^{2} y^{4} + 1

= (10 x^{2} y^{4} - 1) (100 x^{4} y^{8} + 10 x^{2} y^{4} + 1)