因数 16d^2e^2-64m^2

解

因数

16 d^{2} e^{2} - 64 m^{2}

16 (e d + 2 m) (e d - 2 m)

解答ステップ

16 d^{2} e^{2} - 64 m^{2}

16 d^{2} e^{2}

を書き換え

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

64 m^{2}

を書き換え

(2^{3} m)^{2}

= (2^{2} d e)^{2} - (2^{3} m)^{2}

2乗の差の公式を適用する:

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

(2^{2} d e)^{2} - (2^{3} m)^{2} = (2^{2} d e + 2^{3} m) (2^{2} d e - 2^{3} m)

= (2^{2} d e + 2^{3} m) (2^{2} d e - 2^{3} m)

改良

= (4 e d + 8 m) (4 e d - 8 m)

因数

4 e d + 8 m : 4 (e d + 2 m)

= 4 (e d + 2 m) (4 e d - 8 m)

因数

4 e d - 8 m : 4 (e d - 2 m)

= 4 (e d + 2 m) \cdot 4 (e d - 2 m)

改良

= 16 (e d + 2 m) (e d - 2 m)