因数 343v^3+27w^6

解

因数

343 v^{3} + 27 w^{6}

(7 v + 3 w^{2}) (49 v^{2} - 21 v w^{2} + 9 w^{4})

解答ステップ

343 v^{3} + 27 w^{6}

指数の規則を適用する

= (7 v)^{3} + (3 w^{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})

(7 v)^{3} + (3 w^{2})^{3} = (7 v + 3 w^{2}) ((7 v)^{2} - 7 v \cdot 3 w^{2} + (3 w^{2})^{2})

= (7 v + 3 w^{2}) ((7 v)^{2} - 7 v \cdot 3 w^{2} + (3 w^{2})^{2})

簡素化

(7 v)^{2} - 7 v \cdot 3 w^{2} + (3 w^{2})^{2} : 49 v^{2} - 21 v w^{2} + 9 w^{4}

= (7 v + 3 w^{2}) (49 v^{2} - 21 v w^{2} + 9 w^{4})