因数 x^6+y^9

解

因数

x^{6} + y^{9}

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

解答ステップ

x^{6} + y^{9}

指数の規則を適用する

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

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

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

簡素化

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

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