因数 16a^4-4a^2+4a-1

解

因数

16 a^{4} - 4 a^{2} + 4 a - 1

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

解答ステップ

16 a^{4} - 4 a^{2} + 4 a - 1

因数

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

= 16 a^{4} - (2 a - 1)^{2}

簡素化

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

= (4 a^{2})^{2} - (2 a - 1)^{2}

2乗の差の公式を適用する:

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

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

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

簡素化

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

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