因数 m^{24}y^3-n^3z^{24}

解

因数

m^{24} y^{3} - n^{3} z^{24}

(m^{8} y - n z^{8}) (m^{16} y^{2} + n m^{8} y z^{8} + n^{2} z^{16})

解答ステップ

m^{24} y^{3} - n^{3} z^{24}

m^{24} y^{3}

を書き換え

(m^{8} y)^{3}

n^{3} z^{24}

を書き換え

(n z^{8})^{3}

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

= (m^{8} y - n z^{8}) ((n z^{8})^{2} + n z^{8} m^{8} y + (m^{8} y)^{2})

簡素化

(m^{8} y - n z^{8}) ((m^{8} y)^{2} + n z^{8} m^{8} y + (n z^{8})^{2}) : (m^{8} y - n z^{8}) (m^{16} y^{2} + n m^{8} y z^{8} + n^{2} z^{16})

= (m^{8} y - n z^{8}) (m^{16} y^{2} + n m^{8} y z^{8} + n^{2} z^{16})