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

The solution to expand (x+ux)(udx+xdu) is xudx+x^2du+xu^2dx+x^2udu

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expand (x+ux)(udx+xdu)

expand

(x + ux) (u d x + x d u)

xu d x + x^{2} d u + x u^{2} d x + x^{2} u d u

Solution steps

(x + ux) (u d x + x d u)

= (x + xu) (u d x + x d u)

Apply FOIL method:

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

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

= xu d x + xx d u + uxu d x + uxx d u

= xu d x + xx d u + xuu d x + xxu d u

Simplify

xu d x + xx d u + xuu d x + xxu d u : xu d x + x^{2} d u + x u^{2} d x + x^{2} u d u

= xu d x + x^{2} d u + x u^{2} d x + x^{2} u d u

\frac{m - 2}{( m - 3 ) ( m + 2 )}

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

\frac{12 ( x ^{2} + 12 )}{( x ^{2} - 36 ) ^{3}}

(- 4 x + 5) \cdot (2 x + 3)

What is expand (x+ux)(udx+xdu) ?
The solution to expand (x+ux)(udx+xdu) is xudx+x^2du+xu^2dx+x^2udu