因数 9x^{4/7}-1

解

因数

9 x^{\frac{4}{7}} - 1

(3 x^{\frac{2}{7}} + 1) (3 x^{\frac{2}{7}} - 1)

解答ステップ

9 x^{\frac{4}{7}} - 1

x^{\frac{4}{7}}

を書き換え

(7 x)^{4}

= 9 (7 x)^{4} - 1

9 (7 x)^{4} - 1

を書き換え

(3 (7 x)^{2})^{2} - 1^{2}

= (3 (7 x)^{2})^{2} - 1^{2}

2乗の差の公式を適用する:

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

(3 (7 x)^{2})^{2} - 1^{2} = (3 (7 x)^{2} + 1) (3 (7 x)^{2} - 1)

= (3 (7 x)^{2} + 1) (3 (7 x)^{2} - 1)

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

= (3 x^{\frac{2}{7}} + 1) (3 (7 x)^{2} - 1)

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

= (3 x^{\frac{2}{7}} + 1) (3 x^{\frac{2}{7}} - 1)