因数 125q^6-r^6s^3

解

因数

125 q^{6} - r^{6} s^{3}

(5 q^{2} - r^{2} s) (25 q^{4} + 5 q^{2} r^{2} s + r^{4} s^{2})

解答ステップ

125 q^{6} - r^{6} s^{3}

125 q^{6}

を書き換え

(5 q^{2})^{3}

r^{6} s^{3}

を書き換え

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

= (5 q^{2})^{3} - (r^{2} s)^{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 q^{2})^{3} - (r^{2} s)^{3} = (5 q^{2} - r^{2} s) ((5 q^{2})^{2} + 5 q^{2} r^{2} s + (r^{2} s)^{2})

= (5 q^{2} - r^{2} s) ((5 q^{2})^{2} + 5 q^{2} r^{2} s + (r^{2} s)^{2})

簡素化

(5 q^{2} - r^{2} s) ((5 q^{2})^{2} + 5 q^{2} r^{2} s + (r^{2} s)^{2}) : (5 q^{2} - r^{2} s) (25 q^{4} + 5 q^{2} r^{2} s + r^{4} s^{2})

= (5 q^{2} - r^{2} s) (25 q^{4} + 5 q^{2} r^{2} s + r^{4} s^{2})