What is expand (3uy)(udy+ydu) ?

The solution to expand (3uy)(udy+ydu) is 3u^2ydy+3uy^2du

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expand (3uy)(udy+ydu)

expand

(3 u y) (u d y + y d u)

3 u^{2} y d y + 3 u y^{2} d u

Solution steps

(3 u y) (u d y + y d u)

Apply the distributive law:

a (b + c) = ab + a c

a = (3 u y), b = u d y, c = y d u

= (3 u y) u d y + (3 u y) y d u

= u (3 u y) d y + y (3 u y) d u

Simplify

u (3 u y) d y + y (3 u y) d u : 3 u^{2} y d y + 3 u y^{2} d u

= 3 u^{2} y d y + 3 u y^{2} d u

I n (\frac{7 x ^{5}}{y ^{3}})

\frac{( x ^{2} - 5 ) e ^{x}}{( x + 1 )}

(2 x e^{2 x} + e^{2 x} \cdot 2 x^{2})^{6}

\frac{1}{2 ( 1 - cos ( x ) )}

What is expand (3uy)(udy+ydu) ?
The solution to expand (3uy)(udy+ydu) is 3u^2ydy+3uy^2du