因数 25a^2-1/9 b^2

解

因数

25 a^{2} - \frac{1}{9} b^{2}

(5 a + \frac{b}{3}) (5 a - \frac{b}{3})

解答ステップ

25 a^{2} - \frac{1}{9} b^{2}

25 a^{2} = (5 a)^{2}

\frac{1}{9} b^{2} = (\frac{1}{3} b)^{2}

= (5 a)^{2} - (\frac{1}{3} b)^{2}

2乗の差の公式を適用する:

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

(5 a)^{2} - (\frac{1}{3} b)^{2} = (5 a + \frac{1}{3} b) (5 a - \frac{1}{3} b)

= (5 a + \frac{1}{3} b) (5 a - \frac{1}{3} b)

\frac{1}{3} b = \frac{b}{3}

= (5 a + \frac{b}{3}) (5 a - \frac{b}{3})