因数 x^{5/2}-x^{1/2}

解

因数

x^{\frac{5}{2}} - x^{\frac{1}{2}}

x (x + 1) (x + 1) (x - 1)

解答ステップ

x^{\frac{5}{2}} - x^{\frac{1}{2}}

x^{\frac{5}{2}}

を書き換え

(x)^{5}

= (x)^{5} - x^{\frac{1}{2}}

共通項をくくり出す

x : x ((x)^{4} - 1)

= x ((x)^{4} - 1)

因数

(x)^{4} - 1 : ((x)^{2} + 1) (x + 1) (x - 1)

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

簡素化

x ((x)^{2} + 1) (x + 1) (x - 1) : x (x + 1) (x + 1) (x - 1)

= x (x + 1) (x + 1) (x - 1)