What is expand x(x^3-xy^2+2y^3)dy-y(x^3+2y^3)dx ?

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

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expand x(x^3-xy^2+2y^3)dy-y(x^3+2y^3)dx

expand

x (x^{3} - x y^{2} + 2 y^{3}) d y - y (x^{3} + 2 y^{3}) d x

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

Solution steps

x (x^{3} - x y^{2} + 2 y^{3}) d y - y (x^{3} + 2 y^{3}) d x

Expand

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

= x^{4} d y - x^{2} y^{2} d y + 2 x y^{3} d y - y (x^{3} + 2 y^{3}) d x

Expand

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

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

\frac{x}{( x - 2 ) ( x - 3 )}

2 (cos (x) - sin (x))

\frac{s}{( t ^{2} + s ^{2} ) ( t ^{2} + 1 )}

(x - 33) (x + 33)

(1 + 2)^{4}

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