因数 x^3y^3+125z^3

解

因数

x^{3} y^{3} + 125 z^{3}

(x y + 5 z) (x^{2} y^{2} - 5 x yz + 25 z^{2})

解答ステップ

x^{3} y^{3} + 125 z^{3}

x^{3} y^{3}

を書き換え

(x y)^{3}

125 z^{3}

を書き換え

(5 z)^{3}

= (x y)^{3} + (5 z)^{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})

(x y)^{3} + (5 z)^{3} = (x y + 5 z) ((x y)^{2} - x y 5 z + (5 z)^{2})

= (x y + 5 z) ((x y)^{2} - x y 5 z + (5 z)^{2})

簡素化

(x y + 5 z) ((x y)^{2} - x y \cdot 5 z + (5 z)^{2}) : (x y + 5 z) (x^{2} y^{2} - 5 x yz + 25 z^{2})

= (x y + 5 z) (x^{2} y^{2} - 5 x yz + 25 z^{2})