What is expand (-3x-5ux)(udx+xdu) ?

The solution to expand (-3x-5ux)(udx+xdu) is -3xudx-3x^2du-5xu^2dx-5x^2udu

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expand (-3x-5ux)(udx+xdu)

expand

(- 3 x - 5 ux) (u d x + x d u)

- 3 xu d x - 3 x^{2} d u - 5 x u^{2} d x - 5 x^{2} u d u

Solution steps

(- 3 x - 5 ux) (u d x + x d u)

= (- 3 x - 5 xu) (u d x + x d u)

Apply FOIL method:

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

a = - 3 x, b = - 5 ux, c = u d x, d = x d u

= (- 3 x) u d x + (- 3 x) x d u + (- 5 ux) u d x + (- 5 ux) x d u

Apply minus-plus rules

+ (- a) = - a

= - 3 xu d x - 3 xx d u - 5 xuu d x - 5 xxu d u

Simplify

- 3 xu d x - 3 xx d u - 5 xuu d x - 5 xxu d u : - 3 xu d x - 3 x^{2} d u - 5 x u^{2} d x - 5 x^{2} u d u

= - 3 xu d x - 3 x^{2} d u - 5 x u^{2} d x - 5 x^{2} u d u

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

(x - y - z)^{5}

\frac{t ^{n}}{e ^{(s - 3) t}}

l m (4 + a e^{b t})

\frac{d}{d x} ((z) (3 x y + z^{2} x - 7 y))

What is expand (-3x-5ux)(udx+xdu) ?
The solution to expand (-3x-5ux)(udx+xdu) is -3xudx-3x^2du-5xu^2dx-5x^2udu