因数 m^3n^3x^3+1

解

因数

m^{3} n^{3} x^{3} + 1

(mn x + 1) (m^{2} n^{2} x^{2} - mn x + 1)

解答ステップ

m^{3} n^{3} x^{3} + 1

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

を書き換え

(mn x)^{3}

= (mn x)^{3} + 1

1

を書き換え

1^{3}

= (mn x)^{3} + 1^{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})

(mn x)^{3} + 1^{3} = (mn x + 1) ((mn x)^{2} - mn x + 1)

= (mn x + 1) ((mn x)^{2} - mn x + 1)

簡素化

(mn x + 1) ((mn x)^{2} - mn x + 1) : (mn x + 1) (m^{2} n^{2} x^{2} - mn x + 1)

= (mn x + 1) (m^{2} n^{2} x^{2} - mn x + 1)