What is expand (ux-2x)(udx+xdu) ?

The solution to expand (ux-2x)(udx+xdu) is u^2xdx+ux^2du-2uxdx-2x^2du

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expand (ux-2x)(udx+xdu)

expand

(ux - 2 x) (u d x + x d u)

u^{2} x d x + u x^{2} d u - 2 ux d x - 2 x^{2} d u

Solution steps

(ux - 2 x) (u d x + x d u)

Apply FOIL method:

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

a = ux, b = - 2 x, c = u d x, d = x d u

= uxu d x + uxx d u + (- 2 x) u d x + (- 2 x) x d u

Apply minus-plus rules

+ (- a) = - a

= uux d x + uxx d u - 2 ux d x - 2 xx d u

Simplify

uux d x + uxx d u - 2 ux d x - 2 xx d u : u^{2} x d x + u x^{2} d u - 2 ux d x - 2 x^{2} d u

= u^{2} x d x + u x^{2} d u - 2 ux d x - 2 x^{2} d u

(u - 4) u

(4 - 2) (3 - 3, - 2 - 4) (x, y)

(sin (θ) + i cos (θ))^{3}

\frac{5 e ^{x}}{( 5 + e ^{x} ) ^{2}}

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

What is expand (ux-2x)(udx+xdu) ?
The solution to expand (ux-2x)(udx+xdu) is u^2xdx+ux^2du-2uxdx-2x^2du