因数 m^{18}y^3-n^3z^{18}

解

因数

m^{18} y^{3} - n^{3} z^{18}

(m^{6} y - n z^{6}) (m^{12} y^{2} + n m^{6} y z^{6} + n^{2} z^{12})

解答ステップ

m^{18} y^{3} - n^{3} z^{18}

m^{18} y^{3}

を書き換え

(m^{6} y)^{3}

n^{3} z^{18}

を書き換え

(n z^{6})^{3}

= (m^{6} y)^{3} - (n z^{6})^{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})

(m^{6} y)^{3} - (n z^{6})^{3} = (m^{6} y - n z^{6}) ((m^{6} y)^{2} + n z^{6} m^{6} y + (n z^{6})^{2})

= (m^{6} y - n z^{6}) ((n z^{6})^{2} + n z^{6} m^{6} y + (m^{6} y)^{2})

簡素化

(m^{6} y - n z^{6}) ((m^{6} y)^{2} + n z^{6} m^{6} y + (n z^{6})^{2}) : (m^{6} y - n z^{6}) (m^{12} y^{2} + n m^{6} y z^{6} + n^{2} z^{12})

= (m^{6} y - n z^{6}) (m^{12} y^{2} + n m^{6} y z^{6} + n^{2} z^{12})