What is expand 4(uy)sqrt(y)(udy+ydu) ?

The solution to expand 4(uy)sqrt(y)(udy+ydu) is 4u^2ysqrt(y)dy+4uy^2sqrt(y)du

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expand 4(uy)sqrt(y)(udy+ydu)

expand

4 (u y) y (u d y + y d u)

4 u^{2} y y d y + 4 u y^{2} y d u

Solution steps

4 (u y) y (u d y + y d u)

= 4 y (u y) (u d y + y d u)

Apply the distributive law:

a (b + c) = ab + a c

a = 4 (u y) y, b = u d y, c = y d u

= 4 (u y) y u d y + 4 (u y) y y d u

= 4 u y (u y) d y + 4 y y (u y) d u

Simplify

4 u y (u y) d y + 4 y y (u y) d u : 4 u^{2} y y d y + 4 u y^{2} y d u

= 4 u^{2} y y d y + 4 u y^{2} y d u

\frac{3 x ^{2} + 9}{( x + 3 ) ( x - 3 )}

e^{(x^{2} + 1)^{3}}

\frac{2 x + 1}{( x + 2 ) ^{2}}

f (t) - f (t - 3) H (t - 3)

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

What is expand 4(uy)sqrt(y)(udy+ydu) ?
The solution to expand 4(uy)sqrt(y)(udy+ydu) is 4u^2ysqrt(y)dy+4uy^2sqrt(y)du