因数 m^6n^3+p^3q^3

解

因数

m^{6} n^{3} + p^{3} q^{3}

(m^{2} n + pq) (m^{4} n^{2} - m^{2} n pq + p^{2} q^{2})

解答ステップ

m^{6} n^{3} + p^{3} q^{3}

m^{6} n^{3}

を書き換え

(m^{2} n)^{3}

p^{3} q^{3}

を書き換え

(pq)^{3}

= (m^{2} n)^{3} + (pq)^{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^{2} n)^{3} + (pq)^{3} = (m^{2} n + pq) ((m^{2} n)^{2} - m^{2} n pq + (pq)^{2})

= (m^{2} n + pq) ((m^{2} n)^{2} - m^{2} n pq + (pq)^{2})

簡素化

(m^{2} n + pq) ((m^{2} n)^{2} - m^{2} n pq + (pq)^{2}) : (m^{2} n + pq) (m^{4} n^{2} - m^{2} n pq + p^{2} q^{2})

= (m^{2} n + pq) (m^{4} n^{2} - m^{2} n pq + p^{2} q^{2})