因数 8x^6+27y^3z^9

解

因数

8 x^{6} + 27 y^{3} z^{9}

(2 x^{2} + 3 y z^{3}) (4 x^{4} - 6 x^{2} y z^{3} + 9 y^{2} z^{6})

解答ステップ

8 x^{6} + 27 y^{3} z^{9}

8 x^{6}

を書き換え

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

27 y^{3} z^{9}

を書き換え

(3 y z^{3})^{3}

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

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

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

簡素化

(2 x^{2} + 3 y z^{3}) ((2 x^{2})^{2} - 3 y z^{3} \cdot 2 x^{2} + (3 y z^{3})^{2}) : (2 x^{2} + 3 y z^{3}) (4 x^{4} - 6 x^{2} y z^{3} + 9 y^{2} z^{6})

= (2 x^{2} + 3 y z^{3}) (4 x^{4} - 6 x^{2} y z^{3} + 9 y^{2} z^{6})