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

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

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

expand

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

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

Solution steps

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

= (x + 2 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 = 2 ux, c = u d x, d = x d u

= xu d x + xx d u + 2 uxu d x + 2 uxx d u

= xu d x + xx d u + 2 xuu d x + 2 xxu d u

Simplify

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

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

- 3 (12 + y = - 3)

\frac{s u m _{(k = 1)} ( 1 + k )}{( ( 2 + k ) ! )}

5.01 (30 0^{0.499})

(sin (3 t) - e^{- 2 t})^{2}

(x^{3} - 3 x^{2} + 2 x)^{5}

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