What is expand (2x+vx)(vdx+xdv) ?

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

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expand (2x+vx)(vdx+xdv)

expand

(2 x + vx) (v d x + x d v)

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

Solution steps

(2 x + vx) (v d x + x d v)

Apply FOIL method:

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

a = 2 x, b = vx, c = v d x, d = x d v

= 2 xv d x + 2 xx d v + vxv d x + vxx d v

= 2 vx d x + 2 xx d v + vvx d x + vxx d v

Simplify

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

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

(1 + ln (x)) x^{2}

e^{t - 2} cos ((a + b + c) t)

(a + d t - c)^{2}

\frac{4 ( x + y ) ^{2}}{3}

3 + (8 + 4)

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