因数 r^3w^6-125p^{12}

解

因数

r^{3} w^{6} - 125 p^{12}

(r w^{2} - 5 p^{4}) (r^{2} w^{4} + 5 r w^{2} p^{4} + 25 p^{8})

解答ステップ

r^{3} w^{6} - 125 p^{12}

r^{3} w^{6}

を書き換え

(r w^{2})^{3}

125 p^{12}

を書き換え

(5 p^{4})^{3}

= (r w^{2})^{3} - (5 p^{4})^{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})

(r w^{2})^{3} - (5 p^{4})^{3} = (r w^{2} - 5 p^{4}) ((r w^{2})^{2} + r w^{2} 5 p^{4} + (5 p^{4})^{2})

= (r w^{2} - 5 p^{4}) ((r w^{2})^{2} + r w^{2} 5 p^{4} + (5 p^{4})^{2})

簡素化

(r w^{2} - 5 p^{4}) ((r w^{2})^{2} + r w^{2} \cdot 5 p^{4} + (5 p^{4})^{2}) : (r w^{2} - 5 p^{4}) (r^{2} w^{4} + 5 r w^{2} p^{4} + 25 p^{8})

= (r w^{2} - 5 p^{4}) (r^{2} w^{4} + 5 r w^{2} p^{4} + 25 p^{8})