因数 4(a+b)^2+19(a+b)-5

解

因数

4 (a + b)^{2} + 19 (a + b) - 5

(4 (a + b) - 1) (a + b + 5)

解答ステップ

4 (a + b)^{2} + 19 (a + b) - 5

式をグループに分ける

= (4 (a + b)^{2} - (a + b)) + (20 (a + b) - 5)

(a + b)

を

4 (a + b)^{2} - (a + b) : (a + b) (4 (a + b) - 1)

からくくり出す

5

を

20 (a + b) - 5 : 5 (4 (a + b) - 1)

からくくり出す

= (a + b) (4 (a + b) - 1) + 5 (4 (a + b) - 1)

共通項をくくり出す

4 (a + b) - 1

= (4 (a + b) - 1) ((a + b) + 5)

改良

= (a + b + 5) (4 (a + b) - 1)