因数 x^{16}-y^{16}

解

因数

x^{16} - y^{16}

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

解答ステップ

x^{16} - y^{16}

x^{16} = (x^{8})^{2}

y^{16} = (y^{8})^{2}

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

2乗の差の公式を適用する:

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

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

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

因数

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

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