What is expand x(x^2+y^2)^2(ydx-xdy) ?

The solution to expand x(x^2+y^2)^2(ydx-xdy) is x^5ydx+2x^3y^3dx+xy^5dx-x^6dy-2x^4y^2dy-x^2y^4dy

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expand x(x^2+y^2)^2(ydx-xdy)

expand

x (x^{2} + y^{2})^{2} (y d x - x d y)

x^{5} y d x + 2 x^{3} y^{3} d x + x y^{5} d x - x^{6} d y - 2 x^{4} y^{2} d y - x^{2} y^{4} d y

Solution steps

x (x^{2} + y^{2})^{2} (y d x - x d y)

Apply the distributive law:

a (b - c) = ab - a c

a = x (x^{2} + y^{2})^{2}, b = y d x, c = x d y

= x (x^{2} + y^{2})^{2} y d x - x (x^{2} + y^{2})^{2} x d y

= x y (x^{2} + y^{2})^{2} d x - xx (x^{2} + y^{2})^{2} d y

Simplify

x y (x^{2} + y^{2})^{2} d x - xx (x^{2} + y^{2})^{2} d y : x^{5} y d x + 2 x^{3} y^{3} d x + x y^{5} d x - x^{6} d y - 2 x^{4} y^{2} d y - x^{2} y^{4} d y

= x^{5} y d x + 2 x^{3} y^{3} d x + x y^{5} d x - x^{6} d y - 2 x^{4} y^{2} d y - x^{2} y^{4} d y

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

\frac{1}{( x - 11 ) ^{2}}

(x - 1) e^{(x - 1)^{2}}

\frac{( 4 - x ) ( 16 + 5 x ^{2} )}{8}

3 + 3 \frac{3}{4}

What is expand x(x^2+y^2)^2(ydx-xdy) ?
The solution to expand x(x^2+y^2)^2(ydx-xdy) is x^5ydx+2x^3y^3dx+xy^5dx-x^6dy-2x^4y^2dy-x^2y^4dy