因数 343x^3y^3-64z^3

解

因数

343 x^{3} y^{3} - 64 z^{3}

(7 x y - 4 z) (49 x^{2} y^{2} + 28 x yz + 16 z^{2})

解答ステップ

343 x^{3} y^{3} - 64 z^{3}

343 x^{3} y^{3}

を書き換え

(7 x y)^{3}

64 z^{3}

を書き換え

(2^{2} z)^{3}

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

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

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

簡素化

(7 x y - 2^{2} z) ((7 x y)^{2} + 2^{2} z \cdot 7 x y + (2^{2} z)^{2}) : (7 x y - 4 z) (49 x^{2} y^{2} + 28 x yz + 16 z^{2})

= (7 x y - 4 z) (49 x^{2} y^{2} + 28 x yz + 16 z^{2})