因数 x^{12}+y^{12}

解

因数

x^{12} + y^{12}

(x^{4} + y^{4}) (x^{8} - x^{4} y^{4} + y^{8})

解答ステップ

x^{12} + y^{12}

指数の規則を適用する

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

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

簡素化

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

= (x^{4} + y^{4}) (x^{8} - x^{4} y^{4} + y^{8})