因数 e^{30}-1

解

因数

e^{30} - 1

(e + 1) (e^{4} - e^{3} + e^{2} - e + 1) (e - 1) (e^{4} + e^{3} + e^{2} + e + 1) (e^{20} + e^{10} + 1)

解答ステップ

e^{30} - 1

e^{30} - 1

を書き換え

(e^{10})^{3} - 1^{3}

= (e^{10})^{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})

(e^{10})^{3} - 1^{3} = (e^{10} - 1) (e^{20} + e^{10} + 1)

= (e^{10} - 1) (e^{20} + e^{10} + 1)

因数

e^{10} - 1 : (e + 1) (e^{4} - e^{3} + e^{2} - e + 1) (e - 1) (e^{4} + e^{3} + e^{2} + e + 1)

= (e + 1) (e^{4} - e^{3} + e^{2} - e + 1) (e - 1) (e^{4} + e^{3} + e^{2} + e + 1) (e^{20} + e^{10} + 1)