因数 16x^4-4x^2-4x-1

解

因数

16 x^{4} - 4 x^{2} - 4 x - 1

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

解答ステップ

16 x^{4} - 4 x^{2} - 4 x - 1

因数

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

= 16 x^{4} - (2 x + 1)^{2}

簡素化

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

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

2乗の差の公式を適用する:

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

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

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

簡素化

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

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