因数 (x^2-5)^3-64y^3

解

因数

(x^{2} - 5)^{3} - 64 y^{3}

(x^{2} - 5 - 4 y) ((x^{2} - 5)^{2} + 4 y (x^{2} - 5) + 16 y^{2})

解答ステップ

(x^{2} - 5)^{3} - 64 y^{3}

(x^{2} - 5)^{3} - 64 y^{3}

を書き換え

(x^{2} - 5)^{3} - (4 y)^{3}

= (x^{2} - 5)^{3} - (4 y)^{3}

立方数の差の公式を適用する:

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

(x^{2} - 5)^{3} - (4 y)^{3} = ((x^{2} - 5) - 4 y) ((x^{2} - 5)^{2} + 4 (x^{2} - 5) y + 4^{2} y^{2})

= ((x^{2} - 5) - 4 y) ((x^{2} - 5)^{2} + 4 y (x^{2} - 5) + 4^{2} y^{2})

改良

= (x^{2} - 4 y - 5) (16 y^{2} + 4 y (x^{2} - 5) + (x^{2} - 5)^{2})