因数 16x^4-625y^4

解

因数

16 x^{4} - 625 y^{4}

(4 x^{2} + 25 y^{2}) (2 x + 5 y) (2 x - 5 y)

解答ステップ

16 x^{4} - 625 y^{4}

16 x^{4} = (4 x^{2})^{2}

625 y^{4} = (25 y^{2})^{2}

= (4 x^{2})^{2} - (25 y^{2})^{2}

2乗の差の公式を適用する:

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

(4 x^{2})^{2} - (25 y^{2})^{2} = (4 x^{2} + 25 y^{2}) (4 x^{2} - 25 y^{2})

= (4 x^{2} + 25 y^{2}) (4 x^{2} - 25 y^{2})

因数

4 x^{2} - 25 y^{2} : (2 x + 5 y) (2 x - 5 y)

= (4 x^{2} + 25 y^{2}) (2 x + 5 y) (2 x - 5 y)