因数 729u^3s^3-1000t^3

解

因数

729 u^{3} s^{3} - 1000 t^{3}

(9 u s - 10 t) (81 u^{2} s^{2} + 90 u s t + 100 t^{2})

解答ステップ

729 u^{3} s^{3} - 1000 t^{3}

729 u^{3} s^{3}

を書き換え

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

1000 t^{3}

を書き換え

(10 t)^{3}

= (3^{2} u s)^{3} - (10 t)^{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})

(3^{2} u s)^{3} - (10 t)^{3} = (3^{2} u s - 10 t) ((3^{2} u s)^{2} + 10 t 3^{2} u s + (10 t)^{2})

= (3^{2} u s - 10 t) ((10 t)^{2} + 10 t 3^{2} u s + (3^{2} u s)^{2})

簡素化

(3^{2} u s - 10 t) ((3^{2} u s)^{2} + 10 t \cdot 3^{2} u s + (10 t)^{2}) : (9 u s - 10 t) (81 u^{2} s^{2} + 90 u s t + 100 t^{2})

= (9 u s - 10 t) (81 u^{2} s^{2} + 90 u s t + 100 t^{2})