What is expand-x(x^3+y)dy ?

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

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expand-x(x^3+y)dy

expand

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

- x^{4} d y - x y d y

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = - x d y, b = x^{3}, c = y

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

Apply minus-plus rules

+ (- a) = - a

= - x^{3} x d y - x y d y

x^{3} x d y = x^{4} d y

= - x^{4} d y - x y d y

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