展開する (2vx^2+x^2+3v^2x^2)(vdx+xdv)

解

展開する

(2 v x^{2} + x^{2} + 3 v^{2} x^{2}) (v d x + x d v)

2 v^{2} x^{2} d x + 2 v x^{3} d v + v x^{2} d x + x^{3} d v + 3 v^{3} x^{2} d x + 3 v^{2} x^{3} d v

解答ステップ

(2 v x^{2} + x^{2} + 3 v^{2} x^{2}) (v d x + x d v)

括弧を分配する

= 2 v x^{2} v d x + 2 v x^{2} x d v + x^{2} v d x + x^{2} x d v + 3 v^{2} x^{2} v d x + 3 v^{2} x^{2} x d v

= 2 vv x^{2} d x + 2 v x^{2} x d v + v x^{2} d x + x^{2} x d v + 3 v^{2} v x^{2} d x + 3 v^{2} x^{2} x d v

簡素化

2 vv x^{2} d x + 2 v x^{2} x d v + v x^{2} d x + x^{2} x d v + 3 v^{2} v x^{2} d x + 3 v^{2} x^{2} x d v : 2 v^{2} x^{2} d x + 2 v x^{3} d v + v x^{2} d x + x^{3} d v + 3 v^{3} x^{2} d x + 3 v^{2} x^{3} d v

= 2 v^{2} x^{2} d x + 2 v x^{3} d v + v x^{2} d x + x^{3} d v + 3 v^{3} x^{2} d x + 3 v^{2} x^{3} d v