What is expand (1/(x^2)+y^2)(xdy-ydx) ?

The solution to expand (1/(x^2)+y^2)(xdy-ydx) is (dy)/x-(ydx)/(x^2)+xy^2dy-y^3dx

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expand (1/(x^2)+y^2)(xdy-ydx)

expand

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

\frac{d y}{x} - \frac{y d x}{x ^{2}} + x y^{2} d y - y^{3} d x

Solution steps

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

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = \frac{1}{x ^{2}}, b = y^{2}, c = x d y, d = - y d x

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

Apply minus-plus rules

+ (- a) = - a

= \frac{1}{x ^{2}} x d y - \frac{1}{x ^{2}} y d x + x y^{2} d y - y^{2} y d x

Simplify

\frac{1}{x ^{2}} x d y - \frac{1}{x ^{2}} y d x + x y^{2} d y - y^{2} y d x : \frac{d y}{x} - \frac{y d x}{x ^{2}} + x y^{2} d y - y^{3} d x

= \frac{d y}{x} - \frac{y d x}{x ^{2}} + x y^{2} d y - y^{3} d x

- \frac{1}{( z - 1 ) ( z - 2 )}

e (18 e^{- 6 x} + 5)

A (- 3, - 4) B (5, 7)

\frac{( ( x ^{(3)} - 14 x ^{(2)} + 195 x + 128 ) )}{( x )}

3 + 2 i^{2}

What is expand (1/(x^2)+y^2)(xdy-ydx) ?
The solution to expand (1/(x^2)+y^2)(xdy-ydx) is (dy)/x-(ydx)/(x^2)+xy^2dy-y^3dx