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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Expand

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

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

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

(2 x + 2)^{2}

(1 + \frac{3 i}{n})^{3}

\frac{- 2 s + 4}{( s ^{2} + 1 ) ( s - 1 ) ^{2}}

(x^{2})^{3}

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