簡約 (u^2+5u^2v+4uv^2)-(u^2+5u^2v^2+4uv)

解

簡約

(u^{2} + 5 u^{2} v + 4 u v^{2}) - (u^{2} + 5 u^{2} v^{2} + 4 uv)

5 u^{2} v + 4 u v^{2} - 5 u^{2} v^{2} - 4 uv

解答ステップ

(u^{2} + 5 u^{2} v + 4 u v^{2}) - (u^{2} + 5 u^{2} v^{2} + 4 uv)

規則を適用する:

(a) = a

(u^{2} + 5 u^{2} v + 4 u v^{2}) = u^{2} + 5 u^{2} v + 4 u v^{2}

= u^{2} + 5 u^{2} v + 4 u v^{2} - (u^{2} + 5 u^{2} v^{2} + 4 uv)

分配法則を適用する:

- (a + b) = - a - b

- (u^{2} + 5 u^{2} v^{2} + 4 uv) = - u^{2} - 5 u^{2} v^{2} - 4 uv

= u^{2} + 5 u^{2} v + 4 u v^{2} - u^{2} - 5 u^{2} v^{2} - 4 uv

条件のようなグループ

= u^{2} - u^{2} + 5 u^{2} v + 4 u v^{2} - 5 u^{2} v^{2} - 4 uv

類似した元を足す:

u^{2} - u^{2} = 0

= 5 u^{2} v + 4 u v^{2} - 5 u^{2} v^{2} - 4 uv