因数 3ax^3-2bx^3+3a-2b

解

因数

3 a x^{3} - 2 b x^{3} + 3 a - 2 b

(x^{2} + 1 - x) (1 + x) (3 a - 2 b)

解答ステップ

3 a x^{3} - 2 b x^{3} + 3 a - 2 b

書き換え

= 3 a x^{3} - 2 b x^{3} + 1 \cdot 3 a - 2 b

共通項をくくり出す

3 a

= 3 a (x^{3} + 1) - 2 b x^{3} - 2 b

因数

x^{3} + 1 : (x + 1) (x^{2} - x + 1)

= - 2 b x^{3} + 3 a (x + 1) (x^{2} - x + 1) - 2 b

書き換え

= 3 a (1 + x) (x^{2} + 1 - x) - 2 b x^{3} - 1 \cdot 2 b

共通項をくくり出す

2 b

= 3 a (1 + x) (x^{2} + 1 - x) - 2 b (x^{3} + 1)

因数

x^{3} + 1 : (x + 1) (x^{2} - x + 1)

= 3 a (x + 1) (x^{2} - x + 1) - 2 b (x + 1) (x^{2} - x + 1)

共通項をくくり出す

(x^{2} + 1 - x) (1 + x)

= (x^{2} + 1 - x) (1 + x) (3 a - 2 b)