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

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

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

expand

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

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

Solution steps

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

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

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

Distribute parentheses

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

Apply minus-plus rules

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

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

a (- 6, - 2) b (4, 3) c (5, 5) y d (5, - 2)

\frac{x ^{3} + 2 x + 4}{( x - 1 ) ^{2}}

(y = 2, x + 11) - (y = - x + 5)

, - 2 (3 + 4) + 4 (3 - 1) (2 - 7)

\frac{12}{( s - 1 ) ( s ^{2} + 5 s + 6 )}

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