因数 49x^2-100y^4

解

因数

49 x^{2} - 100 y^{4}

(7 x + 10 y^{2}) (7 x - 10 y^{2})

解答ステップ

49 x^{2} - 100 y^{4}

49 x^{2} = (7 x)^{2}

100 y^{4} = (10 y^{2})^{2}

= (7 x)^{2} - (10 y^{2})^{2}

2乗の差の公式を適用する:

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

(7 x)^{2} - (10 y^{2})^{2} = (7 x + 10 y^{2}) (7 x - 10 y^{2})

= (7 x + 10 y^{2}) (7 x - 10 y^{2})