因数 m^{12}n^{24}+x^{18}y^{24}

解

因数

m^{12} n^{24} + x^{18} y^{24}

(m^{4} n^{8} + x^{6} y^{8}) (m^{8} n^{16} - m^{4} n^{8} x^{6} y^{8} + x^{12} y^{16})

解答ステップ

m^{12} n^{24} + x^{18} y^{24}

m^{12} n^{24}

を書き換え

(m n^{2})^{12}

x^{18} y^{24}

を書き換え

(x^{3} y^{4})^{6}

= (m n^{2})^{12} + (x^{3} y^{4})^{6}

(m n^{2})^{12} + (x^{3} y^{4})^{6}

を書き換え

((m n^{2})^{4})^{3} + ((x^{3} y^{4})^{2})^{3}

= ((m n^{2})^{4})^{3} + ((x^{3} y^{4})^{2})^{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})

((m n^{2})^{4})^{3} + ((x^{3} y^{4})^{2})^{3} = ((m n^{2})^{4} + (x^{3} y^{4})^{2}) ((m n^{2})^{8} - (m n^{2})^{4} (x^{3} y^{4})^{2} + (x^{3} y^{4})^{4})

= ((m n^{2})^{4} + (x^{3} y^{4})^{2}) ((m n^{2})^{8} - (m n^{2})^{4} (x^{3} y^{4})^{2} + (x^{3} y^{4})^{4})

簡素化

((m n^{2})^{4} + (x^{3} y^{4})^{2}) ((m n^{2})^{8} - (m n^{2})^{4} (x^{3} y^{4})^{2} + (x^{3} y^{4})^{4}) : (m^{4} n^{8} + x^{6} y^{8}) (m^{8} n^{16} - m^{4} n^{8} x^{6} y^{8} + x^{12} y^{16})

= (m^{4} n^{8} + x^{6} y^{8}) (m^{8} n^{16} - m^{4} n^{8} x^{6} y^{8} + x^{12} y^{16})