因数 125p^6+27

解

因数

125 p^{6} + 27

(5 p^{2} + 3) (25 p^{4} - 15 p^{2} + 9)

解答ステップ

125 p^{6} + 27

指数の規則を適用する

= (5 p^{2})^{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 p^{2})^{3} + 3^{3} = (5 p^{2} + 3) (5^{2} p^{4} - 3 \cdot 5 p^{2} + 3^{2})

= (5 p^{2} + 3) (5^{2} p^{4} - 3 \cdot 5 p^{2} + 3^{2})

簡素化

(5 p^{2} + 3) (5^{2} p^{4} - 3 \cdot 5 p^{2} + 3^{2}) : (5 p^{2} + 3) (25 p^{4} - 15 p^{2} + 9)

= (5 p^{2} + 3) (25 p^{4} - 15 p^{2} + 9)