因数 x^{7/2}-x^{3/2}

解

因数

x^{\frac{7}{2}} - x^{\frac{3}{2}}

x^{\frac{3}{2}} (x + 1) (x + 1) (x - 1)

解答ステップ

x^{\frac{7}{2}} - x^{\frac{3}{2}}

x^{\frac{7}{2}}

を書き換え

(x)^{7}

= (x)^{7} - x^{\frac{3}{2}}

x^{\frac{3}{2}}

を書き換え

(x)^{3}

= (x)^{7} - (x)^{3}

共通項をくくり出す

(x)^{3} : (x)^{3} ((x)^{4} - 1)

= (x)^{3} ((x)^{4} - 1)

因数

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

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

簡素化

(x)^{3} ((x)^{2} + 1) (x + 1) (x - 1) : (x)^{3} (x + 1) (x + 1) (x - 1)

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

(x)^{3} = x^{\frac{3}{2}}

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