因数 x^3y^3-64z^3

解

因数

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

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

解答ステップ

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

x^{3} y^{3}

を書き換え

(x y)^{3}

64 z^{3}

を書き換え

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

= (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})

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

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

簡素化

(x y - 2^{2} z) ((x y)^{2} + 2^{2} z x y + (2^{2} z)^{2}) : (x y - 4 z) (x^{2} y^{2} + 4 x yz + 16 z^{2})

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