因数 r^8-4r^4+4r^2-1

解

因数

r^{8} - 4 r^{4} + 4 r^{2} - 1

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

解答ステップ

r^{8} - 4 r^{4} + 4 r^{2} - 1

u =

にする

r^{2}

= u^{4} - 4 u^{2} + 4 u - 1

因数

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

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

代用を戻す

u = r^{2}

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

因数

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

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

因数

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

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

改良

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