因数 625x^4-16y^4

解

因数

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

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

解答ステップ

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

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

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

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

2乗の差の公式を適用する:

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

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

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

因数

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

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