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

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

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

expand

(3 x + vx) (v d x + x d v)

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

Solution steps

(3 x + vx) (v d x + x d v)

Apply FOIL method:

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

a = 3 x, b = vx, c = v d x, d = x d v

= 3 xv d x + 3 xx d v + vxv d x + vxx d v

= 3 vx d x + 3 xx d v + vvx d x + vxx d v

Simplify

3 vx d x + 3 xx d v + vvx d x + vxx d v : 3 vx d x + 3 x^{2} d v + v^{2} x d x + v x^{2} d v

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

\frac{( 4 x + 1 ) ( 5 x - 1 )}{x ^{2} - 4}

Q_{0} (1 - e^{- \frac{y}{a}})

\frac{( x + 1 ) ( x - 4 )}{x - 1}

\frac{9 - 4 y}{4}

\frac{3 x + 1}{x ( 9 - x )}

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