展开 (6x^2-8x^2v+v^2x^2)(vdx+xdv)

解答

展开

(6 x^{2} - 8 x^{2} v + v^{2} x^{2}) (v d x + x d v)

6 v x^{2} d x + 6 x^{3} d v - 8 v^{2} x^{2} d x - 8 v x^{3} d v + v^{3} x^{2} d x + v^{2} x^{3} d v

求解步骤

(6 x^{2} - 8 x^{2} v + v^{2} x^{2}) (v d x + x d v)

= (6 x^{2} - 8 v x^{2} + v^{2} x^{2}) (v d x + x d v)

打开括号

= 6 x^{2} v d x + 6 x^{2} x d v + (- 8 x^{2} v) v d x + (- 8 x^{2} v) x d v + v^{2} x^{2} v d x + v^{2} x^{2} x d v

使用加减运算法则

+ (- a) = - a

= 6 v x^{2} d x + 6 x^{2} x d v - 8 vv x^{2} d x - 8 v x^{2} x d v + v^{2} v x^{2} d x + v^{2} x^{2} x d v

化简

6 v x^{2} d x + 6 x^{2} x d v - 8 vv x^{2} d x - 8 v x^{2} x d v + v^{2} v x^{2} d x + v^{2} x^{2} x d v : 6 v x^{2} d x + 6 x^{3} d v - 8 v^{2} x^{2} d x - 8 v x^{3} d v + v^{3} x^{2} d x + v^{2} x^{3} d v

= 6 v x^{2} d x + 6 x^{3} d v - 8 v^{2} x^{2} d x - 8 v x^{3} d v + v^{3} x^{2} d x + v^{2} x^{3} d v

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