因数 625x^4-1

解

因数

625 x^{4} - 1

(25 x^{2} + 1) (5 x + 1) (5 x - 1)

解答ステップ

625 x^{4} - 1

指数の規則を適用する

= (25 x^{2})^{2} - 1^{2}

2乗の差の公式を適用する:

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

(25 x^{2})^{2} - 1^{2} = (25 x^{2} + 1) (25 x^{2} - 1)

= (25 x^{2} + 1) (25 x^{2} - 1)

因数

25 x^{2} - 1 : (5 x + 1) (5 x - 1)

= (25 x^{2} + 1) (5 x + 1) (5 x - 1)