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

The solution to expand-(x-sqrt(x^2+y^2))^2dy is -2x^2dy+2xdysqrt(x^2+y^2)-y^2dy

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expand-(x-sqrt(x^2+y^2))^2dy

expand

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

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

Solution steps

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

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

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

\frac{1 - x}{( 2 x - 1 ) ( 4 - x )}

(- 2)^{2}

\frac{x}{12} - 1.5 y

\frac{( x + 82 ) ( x + 40 )}{2}

\frac{( x + 87 ) ( x + 20 )}{2}

What is expand-(x-sqrt(x^2+y^2))^2dy ?
The solution to expand-(x-sqrt(x^2+y^2))^2dy is -2x^2dy+2xdysqrt(x^2+y^2)-y^2dy