因数 216x^3y^3-343z^3

解

因数

216 x^{3} y^{3} - 343 z^{3}

(6 x y - 7 z) (36 x^{2} y^{2} + 42 x yz + 49 z^{2})

解答ステップ

216 x^{3} y^{3} - 343 z^{3}

216 x^{3} y^{3}

を書き換え

(6 x y)^{3}

343 z^{3}

を書き換え

(7 z)^{3}

= (6 x y)^{3} - (7 z)^{3}

立方数の差の公式を適用する:

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

(6 x y)^{3} - (7 z)^{3} = (6 x y - 7 z) ((6 x y)^{2} + 7 z 6 x y + (7 z)^{2})

= (6 x y - 7 z) ((7 z)^{2} + 7 z 6 x y + (6 x y)^{2})

簡素化

(6 x y - 7 z) ((6 x y)^{2} + 7 z \cdot 6 x y + (7 z)^{2}) : (6 x y - 7 z) (36 x^{2} y^{2} + 42 x yz + 49 z^{2})

= (6 x y - 7 z) (36 x^{2} y^{2} + 42 x yz + 49 z^{2})