What is expand-(1+4v+4v^2)(vdx+xdv) ?

The solution to expand-(1+4v+4v^2)(vdx+xdv) is -vdx-xdv-4v^2dx-4vxdv-4v^3dx-4v^2xdv

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expand-(1+4v+4v^2)(vdx+xdv)

expand

- (1 + 4 v + 4 v^{2}) (v d x + x d v)

- v d x - x d v - 4 v^{2} d x - 4 vx d v - 4 v^{3} d x - 4 v^{2} x d v

Solution steps

- (1 + 4 v + 4 v^{2}) (v d x + x d v)

Expand

(1 + 4 v + 4 v^{2}) (v d x + x d v) : v d x + x d v + 4 v^{2} d x + 4 vx d v + 4 v^{3} d x + 4 v^{2} x d v

= - (v d x + x d v + 4 v^{2} d x + 4 vx d v + 4 v^{3} d x + 4 v^{2} x d v)

Distribute parentheses

= - (v d x) - (x d v) - (4 v^{2} d x) - (4 vx d v) - (4 v^{3} d x) - (4 v^{2} x d v)

Apply minus-plus rules

+ (- a) = - a

= - v d x - x d v - 4 v^{2} d x - 4 vx d v - 4 v^{3} d x - 4 v^{2} x d v

\frac{- 16 x - 8 h}{x ^{2} ( x + h ) ^{2}}

(3 + e^{- 6 t})^{2}

\frac{3 x ( h - 1 )}{h}

\frac{P ( a l - a c ) c}{l ^{2}}

3 (x + 5 = 8 x + 15 - 5 x)

What is expand-(1+4v+4v^2)(vdx+xdv) ?
The solution to expand-(1+4v+4v^2)(vdx+xdv) is -vdx-xdv-4v^2dx-4vxdv-4v^3dx-4v^2xdv