因数 1-4/9 a^8

解

因数

1 - \frac{4}{9} a^{8}

(1 + \frac{2}{3} a^{4}) (1 - \frac{2}{3} a^{4})

解答ステップ

1 - \frac{4}{9} a^{8}

1 = 1^{2}

\frac{4}{9} a^{8} = (\frac{2}{3} a^{4})^{2}

= 1^{2} - (\frac{2}{3} a^{4})^{2}

2乗の差の公式を適用する:

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

1^{2} - (\frac{2}{3} a^{4})^{2} = (1 + \frac{2}{3} a^{4}) (1 - \frac{2}{3} a^{4})

= (1 + \frac{2}{3} a^{4}) (1 - \frac{2}{3} a^{4})