因数+20(4a+b)^2-45(2a-3b)^2

解

因数

+ 20 (4 a + b)^{2} - 45 (2 a - 3 b)^{2}

35 (2 a - b) (2 a + 11 b)

解答ステップ

20 (4 a + b)^{2} - 45 (2 a - 3 b)^{2}

共通項をくくり出す

5 : 5 (4 (4 a + b)^{2} - 9 (2 a - 3 b)^{2})

= 5 (4 (4 a + b)^{2} - 9 (2 a - 3 b)^{2})

因数

4 (4 a + b)^{2} - 9 (2 a - 3 b)^{2} : 7 (2 a - b) (2 a + 11 b)

= 5 \cdot 7 (2 a - b) (2 a + 11 b)

数を乗じる:

5 \cdot 7 = 35

= 35 (2 a - b) (2 a + 11 b)