因数 1331x^6y^9+216a^{12}b^{15}

解

因数

1331 x^{6} y^{9} + 216 a^{12} b^{15}

(11 x^{2} y^{3} + 6 a^{4} b^{5}) (121 x^{4} y^{6} - 66 a^{4} b^{5} x^{2} y^{3} + 36 a^{8} b^{10})

解答ステップ

1331 x^{6} y^{9} + 216 a^{12} b^{15}

1331 x^{6} y^{9}

を書き換え

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

216 a^{12} b^{15}

を書き換え

(6 a^{4} b^{5})^{3}

= (11 x^{2} y^{3})^{3} + (6 a^{4} b^{5})^{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})

(11 x^{2} y^{3})^{3} + (6 a^{4} b^{5})^{3} = (11 x^{2} y^{3} + 6 a^{4} b^{5}) ((11 x^{2} y^{3})^{2} - 6 a^{4} b^{5} 11 x^{2} y^{3} + (6 a^{4} b^{5})^{2})

= (6 a^{4} b^{5} + 11 x^{2} y^{3}) ((6 a^{4} b^{5})^{2} - 6 a^{4} b^{5} 11 x^{2} y^{3} + (11 x^{2} y^{3})^{2})

簡素化

(11 x^{2} y^{3} + 6 a^{4} b^{5}) ((11 x^{2} y^{3})^{2} - 6 a^{4} b^{5} \cdot 11 x^{2} y^{3} + (6 a^{4} b^{5})^{2}) : (11 x^{2} y^{3} + 6 a^{4} b^{5}) (121 x^{4} y^{6} - 66 a^{4} b^{5} x^{2} y^{3} + 36 a^{8} b^{10})

= (11 x^{2} y^{3} + 6 a^{4} b^{5}) (121 x^{4} y^{6} - 66 a^{4} b^{5} x^{2} y^{3} + 36 a^{8} b^{10})