因数 125m^3+27

解

因数

125 m^{3} + 27

(5 m + 3) (25 m^{2} - 15 m + 9)

解答ステップ

125 m^{3} + 27

指数の規則を適用する

= (5 m)^{3} + 3^{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})

(5 m)^{3} + 3^{3} = (5 m + 3) (5^{2} m^{2} - 3 \cdot 5 m + 3^{2})

= (5 m + 3) (5^{2} m^{2} - 3 \cdot 5 m + 3^{2})

簡素化

(5 m + 3) (5^{2} m^{2} - 3 \cdot 5 m + 3^{2}) : (5 m + 3) (25 m^{2} - 15 m + 9)

= (5 m + 3) (25 m^{2} - 15 m + 9)