因数 x^8-81y^8

解

因数

x^{8} - 81 y^{8}

(x^{4} + 9 y^{4}) (x^{2} + 3 y^{2}) (x^{2} - 3 y^{2})

解答ステップ

x^{8} - 81 y^{8}

x^{8} = (x^{4})^{2}

81 y^{8} = (9 y^{4})^{2}

= (x^{4})^{2} - (9 y^{4})^{2}

2乗の差の公式を適用する:

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

(x^{4})^{2} - (9 y^{4})^{2} = (x^{4} + 9 y^{4}) (x^{4} - 9 y^{4})

= (x^{4} + 9 y^{4}) (x^{4} - 9 y^{4})

因数

x^{4} - 9 y^{4} : (x^{2} + 3 y^{2}) (x^{2} - 3 y^{2})

= (x^{4} + 9 y^{4}) (x^{2} + 3 y^{2}) (x^{2} - 3 y^{2})