因数 64x^3y^9-125z^3w^6

解

因数

64 x^{3} y^{9} - 125 z^{3} w^{6}

(4 x y^{3} - 5 z w^{2}) (16 x^{2} y^{6} + 20 x y^{3} z w^{2} + 25 z^{2} w^{4})

解答ステップ

64 x^{3} y^{9} - 125 z^{3} w^{6}

64 x^{3} y^{9}

を書き換え

(2^{2} x y^{3})^{3}

125 z^{3} w^{6}

を書き換え

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

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

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

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

簡素化

(2^{2} x y^{3} - 5 z w^{2}) ((2^{2} x y^{3})^{2} + 5 z w^{2} \cdot 2^{2} x y^{3} + (5 z w^{2})^{2}) : (4 x y^{3} - 5 z w^{2}) (16 x^{2} y^{6} + 20 x y^{3} z w^{2} + 25 z^{2} w^{4})

= (4 x y^{3} - 5 z w^{2}) (16 x^{2} y^{6} + 20 x y^{3} z w^{2} + 25 z^{2} w^{4})