因数 216m^3-n^{21}p^9

解

因数

216 m^{3} - n^{21} p^{9}

(6 m - n^{7} p^{3}) (36 m^{2} + 6 m n^{7} p^{3} + n^{14} p^{6})

解答ステップ

216 m^{3} - n^{21} p^{9}

216 m^{3}

を書き換え

(6 m)^{3}

n^{21} p^{9}

を書き換え

(n^{7} p^{3})^{3}

= (6 m)^{3} - (n^{7} p^{3})^{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})

(6 m)^{3} - (n^{7} p^{3})^{3} = (6 m - n^{7} p^{3}) ((6 m)^{2} + 6 m n^{7} p^{3} + (n^{7} p^{3})^{2})

= (6 m - n^{7} p^{3}) ((6 m)^{2} + 6 m n^{7} p^{3} + (n^{7} p^{3})^{2})

簡素化

(6 m - n^{7} p^{3}) ((6 m)^{2} + 6 m n^{7} p^{3} + (n^{7} p^{3})^{2}) : (6 m - n^{7} p^{3}) (36 m^{2} + 6 m n^{7} p^{3} + n^{14} p^{6})

= (6 m - n^{7} p^{3}) (36 m^{2} + 6 m n^{7} p^{3} + n^{14} p^{6})