因数 9x^6-y^8

解

因数

9 x^{6} - y^{8}

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

解答ステップ

9 x^{6} - y^{8}

9 x^{6} = (3 x^{3})^{2}

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

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

2乗の差の公式を適用する:

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

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

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