因数 27w^3+y^6

解

因数

27 w^{3} + y^{6}

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

解答ステップ

27 w^{3} + y^{6}

指数の規則を適用する

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

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

簡素化

(3 w)^{2} - 3 w y^{2} + (y^{2})^{2} : 9 w^{2} - 3 w y^{2} + y^{4}

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