What is expand (vx+vx^3)(vdx+xdv) ?

The solution to expand (vx+vx^3)(vdx+xdv) is v^2xdx+vx^2dv+v^2x^3dx+vx^4dv

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expand (vx+vx^3)(vdx+xdv)

expand

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

v^{2} x d x + v x^{2} d v + v^{2} x^{3} d x + v x^{4} d v

Solution steps

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

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = vx, b = v x^{3}, c = v d x, d = x d v

= vxv d x + vxx d v + v x^{3} v d x + v x^{3} x d v

= vvx d x + vxx d v + vv x^{3} d x + v x^{3} x d v

Simplify

vvx d x + vxx d v + vv x^{3} d x + v x^{3} x d v : v^{2} x d x + v x^{2} d v + v^{2} x^{3} d x + v x^{4} d v

= v^{2} x d x + v x^{2} d v + v^{2} x^{3} d x + v x^{4} d v

\frac{s}{( s - 2 ) ( s ^{2} + 25 )}

\frac{2 ( 7 - 13 )}{3}

3 (2 - e^{\frac{1}{5}})

(5 - 3 x)^{3} d x

5 + 3 x^{2} - \frac{3}{3} \cdot 2 + \frac{( 5 + 7 )}{2}

What is expand (vx+vx^3)(vdx+xdv) ?
The solution to expand (vx+vx^3)(vdx+xdv) is v^2xdx+vx^2dv+v^2x^3dx+vx^4dv