因数 2u(2u-3)^2+u^2(3-2u)

解

因数

2 u (2 u - 3)^{2} + u^{2} (3 - 2 u)

3 u (2 u - 3) (u - 2)

解答ステップ

2 u (2 u - 3)^{2} + u^{2} (3 - 2 u)

u^{2} (3 - 2 u) = - u^{2} (2 u - 3)

= 2 u (2 u - 3)^{2} - u^{2} (2 u - 3)

共通項をくくり出す

u (2 u - 3) : u (2 u - 3) (2 (2 u - 3) - u)

= u (2 u - 3) (2 (2 u - 3) - u)

拡張

2 (2 u - 3) - u : 3 u - 6

= u (2 u - 3) (3 u - 6)

因数

3 u - 6 : 3 (u - 2)

= u (2 u - 3) \cdot 3 (u - 2)

= 3 u (2 u - 3) (u - 2)