因数 5832m^{15}n^{24}+p^{21}

解

因数

5832 m^{15} n^{24} + p^{21}

(18 m^{5} n^{8} + p^{7}) (324 m^{10} n^{16} - 18 m^{5} n^{8} p^{7} + p^{14})

解答ステップ

5832 m^{15} n^{24} + p^{21}

5832 m^{15} n^{24}

を書き換え

(18 m^{5} n^{8})^{3}

= (18 m^{5} n^{8})^{3} + p^{21}

指数の規則を適用する:

a^{b c} = (a^{b})^{c}

p^{21} = (p^{7})^{3}

= (18 m^{5} n^{8})^{3} + (p^{7})^{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})

(18 m^{5} n^{8})^{3} + (p^{7})^{3} = (18 m^{5} n^{8} + p^{7}) ((18 m^{5} n^{8})^{2} - p^{7} 18 m^{5} n^{8} + p^{14})

= (p^{7} + 18 m^{5} n^{8}) (p^{14} - p^{7} 18 m^{5} n^{8} + (18 m^{5} n^{8})^{2})

簡素化

(18 m^{5} n^{8} + p^{7}) ((18 m^{5} n^{8})^{2} - p^{7} \cdot 18 m^{5} n^{8} + p^{14}) : (18 m^{5} n^{8} + p^{7}) (324 m^{10} n^{16} - 18 m^{5} n^{8} p^{7} + p^{14})

= (18 m^{5} n^{8} + p^{7}) (324 m^{10} n^{16} - 18 m^{5} n^{8} p^{7} + p^{14})