因数 5(a+b)^2+19(a+b)-4

解

因数

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

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

解答ステップ

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

式をグループに分ける

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

(a + b)

を

5 (a + b)^{2} - (a + b) : (a + b) (5 (a + b) - 1)

からくくり出す

4

を

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

からくくり出す

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

共通項をくくり出す

5 (a + b) - 1

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

改良

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