因数 9d^2e^8-100f^6g^4

解

因数

9 d^{2} e^{8} - 100 f^{6} g^{4}

(3 e^{4} d + 10 f^{3} g^{2}) (3 e^{4} d - 10 f^{3} g^{2})

解答ステップ

9 d^{2} e^{8} - 100 f^{6} g^{4}

9 d^{2} e^{8}

を書き換え

(3 d e^{4})^{2}

100 f^{6} g^{4}

を書き換え

(10 f^{3} g^{2})^{2}

= (3 d e^{4})^{2} - (10 f^{3} g^{2})^{2}

2乗の差の公式を適用する:

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

(3 d e^{4})^{2} - (10 f^{3} g^{2})^{2} = (3 d e^{4} + 10 f^{3} g^{2}) (3 d e^{4} - 10 f^{3} g^{2})

= (3 d e^{4} + 10 f^{3} g^{2}) (3 d e^{4} - 10 f^{3} g^{2})