因数 x^6-1

解

因数

x^{6} - 1

(x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1)

解答ステップ

x^{6} - 1

指数の規則を適用する

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

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

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

因数

x^{2} - 1 : (x + 1) (x - 1)

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

因数

x^{4} + x^{2} + 1 : (x^{2} + 1 + x) (x^{2} + 1 - x)

= (x + 1) (x - 1) (x^{2} + 1 + x) (x^{2} + 1 - x)

= (x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1)