因数-x^{16}z^{16}+y^{16}

解

因数

- x^{16} z^{16} + y^{16}

(y^{8} + x^{8} z^{8}) (y^{4} + x^{4} z^{4}) (y^{2} + x^{2} z^{2}) (y + x z) (y - x z)

解答ステップ

- x^{16} z^{16} + y^{16}

x^{16} z^{16}

を書き換え

(x z)^{16}

= - (x z)^{16} + y^{16}

y^{16} - (x z)^{16}

を書き換え

(y^{8})^{2} - ((x z)^{8})^{2}

= (y^{8})^{2} - ((x z)^{8})^{2}

2乗の差の公式を適用する:

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

(y^{8})^{2} - ((x z)^{8})^{2} = (y^{8} + (x z)^{8}) (y^{8} - (x z)^{8})

= (y^{8} + (x z)^{8}) (y^{8} - (x z)^{8})

因数

y^{8} - (x z)^{8} : (y^{4} + (x z)^{4}) (y^{2} + (x z)^{2}) (y + x z) (y - x z)

= (y^{8} + (x z)^{8}) (y^{4} + (x z)^{4}) (y^{2} + (x z)^{2}) (y + x z) (y - x z)

簡素化

(y^{8} + (x z)^{8}) (y^{4} + (x z)^{4}) (y^{2} + (x z)^{2}) (y + x z) (y - x z) : (y^{8} + x^{8} z^{8}) (y^{4} + x^{4} z^{4}) (y^{2} + x^{2} z^{2}) (y + x z) (y - x z)

= (y^{8} + x^{8} z^{8}) (y^{4} + x^{4} z^{4}) (y^{2} + x^{2} z^{2}) (y + x z) (y - x z)