因数 (x^2+1)^2-4x^2

解

因数

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

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

解答ステップ

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

簡素化

4 x^{2} : (2 x)^{2}

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

2乗の差の公式を適用する:

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

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

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

規則を適用する:

(a) = a

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

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

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

因数

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

因数

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

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