因数 (5a+3b)^2-20an-12bn

解

因数

(5 a + 3 b)^{2} - 20 an - 12 bn

(3 b + 5 a) (3 b + 5 a - 4 n)

解答ステップ

(5 a + 3 b)^{2} - 20 an - 12 bn

書き換え

= (3 b + 5 a)^{2} - 5 \cdot 4 na - 3 \cdot 4 nb

共通項をくくり出す

4 n

= (3 b + 5 a)^{2} - 4 n (5 a + 3 b)

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

(3 b + 5 a)^{2} = (3 b + 5 a) (3 b + 5 a)

= (3 b + 5 a) (3 b + 5 a) - 4 n (3 b + 5 a)

共通項をくくり出す

(3 b + 5 a)

= (3 b + 5 a) (3 b + 5 a - 4 n)