因数 u^6-64y^6

解

因数

u^{6} - 64 y^{6}

(u + 2 y) (u^{2} - 2 u y + 4 y^{2}) (u - 2 y) (u^{2} + 2 u y + 4 y^{2})

解答ステップ

u^{6} - 64 y^{6}

u^{6} = (u^{3})^{2}

64 y^{6} = (8 y^{3})^{2}

= (u^{3})^{2} - (8 y^{3})^{2}

2乗の差の公式を適用する:

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

(u^{3})^{2} - (8 y^{3})^{2} = (u^{3} + 8 y^{3}) (u^{3} - 8 y^{3})

= (u^{3} + 8 y^{3}) (u^{3} - 8 y^{3})

因数

u^{3} + 8 y^{3} : (u + 2 y) (u^{2} - 2 u y + 4 y^{2})

= (u + 2 y) (u^{2} - 2 u y + 4 y^{2}) (u^{3} - 8 y^{3})

因数

u^{3} - 8 y^{3} : (u - 2 y) (u^{2} + 2 u y + 4 y^{2})

= (u + 2 y) (u^{2} - 2 u y + 4 y^{2}) (u - 2 y) (u^{2} + 2 u y + 4 y^{2})