因数 x^4-y^2-2x^2+1

解

因数

x^{4} - y^{2} - 2 x^{2} + 1

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

解答ステップ

x^{4} - y^{2} - 2 x^{2} + 1

因数

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

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

指数の規則を適用する:

a^{n} b^{n} = (a \cdot b)^{n}

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

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

2乗の差の公式を適用する:

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

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

= ((x + 1) (x - 1) + y) ((x + 1) (x - 1) - y)

簡素化

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

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