因数 p^8-16

解

因数

p^{8} - 16

(p^{2} + 2 p + 2) (p^{2} - 2 p + 2) (p^{2} + 2) (p^{2} - 2)

解答ステップ

p^{8} - 16

指数の規則を適用する

= (p^{4})^{2} - 4^{2}

2乗の差の公式を適用する:

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

(p^{4})^{2} - 4^{2} = (p^{4} + 4) (p^{4} - 4)

= (p^{4} + 4) (p^{4} - 4)

因数

p^{4} + 4 : (p^{2} + 2 p + 2) (p^{2} - 2 p + 2)

= (p^{2} + 2 p + 2) (p^{2} - 2 p + 2) (p^{4} - 4)

因数

p^{4} - 4 : (p^{2} + 2) (p^{2} - 2)

= (p^{2} + 2 p + 2) (p^{2} - 2 p + 2) (p^{2} + 2) (p^{2} - 2)