因数 20d^2-45e^2

解

因数

20 d^{2} - 45 e^{2}

5 (2 d + 3 e) (2 d - 3 e)

解答ステップ

20 d^{2} - 45 e^{2}

20 d^{2} - 45 e^{2}

を書き換え

(20 d)^{2} - (45 e^{2})^{2}

= (20 d)^{2} - (45 e^{2})^{2}

2乗の差の公式を適用する:

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

(20 d)^{2} - (45 e^{2})^{2} = (20 d + 45 e^{2}) (20 d - 45 e^{2})

= (20 d + 45 e^{2}) (20 d - 45 e^{2})

改良

= (25 d + 35 e) (25 d - 35 e)

因数

25 d + 35 e : 5 (2 d + 3 e)

= 5 (2 d + 3 e) (25 d - 35 e)

因数

25 d - 35 e : 5 (2 d - 3 e)

= 5 (2 d + 3 e) 5 (2 d - 3 e)

改良

= 5 (2 d + 3 e) (2 d - 3 e)