因数 m^3-n^3x^3

解

因数

m^{3} - n^{3} x^{3}

(m - n x) (m^{2} + mn x + n^{2} x^{2})

解答ステップ

m^{3} - n^{3} x^{3}

n^{3} x^{3}

を書き換え

(n x)^{3}

= m^{3} - (n x)^{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})

m^{3} - (n x)^{3} = (m - n x) (m^{2} + n x m + (n x)^{2})

= (m - n x) ((n x)^{2} + n x m + m^{2})

簡素化

(m - n x) (m^{2} + n x m + (n x)^{2}) : (m - n x) (m^{2} + mn x + n^{2} x^{2})

= (m - n x) (m^{2} + mn x + n^{2} x^{2})