因数 100x^2y^8-49z^4

解

因数

100 x^{2} y^{8} - 49 z^{4}

(10 x y^{4} + 7 z^{2}) (10 x y^{4} - 7 z^{2})

解答ステップ

100 x^{2} y^{8} - 49 z^{4}

100 x^{2} y^{8} = (10 x y^{4})^{2}

49 z^{4} = (7 z^{2})^{2}

= (10 x y^{4})^{2} - (7 z^{2})^{2}

2乗の差の公式を適用する:

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

(10 x y^{4})^{2} - (7 z^{2})^{2} = (10 x y^{4} + 7 z^{2}) (10 x y^{4} - 7 z^{2})

= (10 x y^{4} + 7 z^{2}) (10 x y^{4} - 7 z^{2})