因数 27x^6+8y^3

解

因数

27 x^{6} + 8 y^{3}

(3 x^{2} + 2 y) (9 x^{4} - 6 x^{2} y + 4 y^{2})

解答ステップ

27 x^{6} + 8 y^{3}

指数の規則を適用する

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

立方数の和の公式を適用する:

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

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

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

簡素化

(3 x^{2})^{2} - 3 x^{2} \cdot 2 y + (2 y)^{2} : 9 x^{4} - 6 x^{2} y + 4 y^{2}

= (3 x^{2} + 2 y) (9 x^{4} - 6 x^{2} y + 4 y^{2})