因数 125a^3b^3-343c^6

解

因数

125 a^{3} b^{3} - 343 c^{6}

(5 ab - 7 c^{2}) (25 a^{2} b^{2} + 35 ab c^{2} + 49 c^{4})

解答ステップ

125 a^{3} b^{3} - 343 c^{6}

125 a^{3} b^{3}

を書き換え

(5 ab)^{3}

343 c^{6}

を書き換え

(7 c^{2})^{3}

= (5 ab)^{3} - (7 c^{2})^{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})

(5 ab)^{3} - (7 c^{2})^{3} = (5 ab - 7 c^{2}) ((5 ab)^{2} + 5 ab 7 c^{2} + (7 c^{2})^{2})

= (5 ab - 7 c^{2}) ((5 ab)^{2} + 5 ab 7 c^{2} + (7 c^{2})^{2})

簡素化

(5 ab - 7 c^{2}) ((5 ab)^{2} + 5 ab \cdot 7 c^{2} + (7 c^{2})^{2}) : (5 ab - 7 c^{2}) (25 a^{2} b^{2} + 35 ab c^{2} + 49 c^{4})

= (5 ab - 7 c^{2}) (25 a^{2} b^{2} + 35 ab c^{2} + 49 c^{4})