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

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

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expand (x^2-v^2x^2)(vdx+xdv)

expand

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

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

Solution steps

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

Apply FOIL method:

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

a = x^{2}, b = - v^{2} x^{2}, c = v d x, d = x d v

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

v x^{2} d x + x^{2} x d v - v^{2} v x^{2} d x - v^{2} x^{2} x d v : v x^{2} d x + x^{3} d v - v^{3} x^{2} d x - v^{2} x^{3} d v

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

\frac{z x ^{2} - z ^{2}}{4} + \frac{z ( P - z - 2 x )}{2}

(F (2) = 5 (2)^{3} - 2 (2)^{2} + 3 x - 1) (x - 1) (x + 3)

(x - 6 + 7) (x - 6 - 7)

(8 x^{2} + 4 x 4 x^{2} - 1 - 1) (1 - x)

\frac{3 ( 4 x + 1 )}{2}

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