What is expand (x^2+y^2+1)dx+x(x-2y)dy ?

The solution to expand (x^2+y^2+1)dx+x(x-2y)dy is x^2dx+y^2dx+dx+x^2dy-2xydy

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expand (x^2+y^2+1)dx+x(x-2y)dy

expand

(x^{2} + y^{2} + 1) d x + x (x - 2 y) d y

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

Solution steps

(x^{2} + y^{2} + 1) d x + x (x - 2 y) d y

Expand

d x (x^{2} + y^{2} + 1) : x^{2} d x + y^{2} d x + d x

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

Expand

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

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

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

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

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

(T - b) (T - c) (T - d) (T - e) (T - f)

What is expand (x^2+y^2+1)dx+x(x-2y)dy ?
The solution to expand (x^2+y^2+1)dx+x(x-2y)dy is x^2dx+y^2dx+dx+x^2dy-2xydy