What is expand (x(4ydx+2xdy)+y^3(3yx+5xdy))(x^2y^3) ?

The solution to expand (x(4ydx+2xdy)+y^3(3yx+5xdy))(x^2y^3) is 4x^3y^4dx+2x^4y^3dy+3x^3y^7+5x^3y^6dy

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expand (x(4ydx+2xdy)+y^3(3yx+5xdy))(x^2y^3)

expand

(x (4 y d x + 2 x d y) + y^{3} (3 y x + 5 x d y)) (x^{2} y^{3})

4 x^{3} y^{4} d x + 2 x^{4} y^{3} d y + 3 x^{3} y^{7} + 5 x^{3} y^{6} d y

Solution steps

(x (4 y d x + 2 x d y) + y^{3} (3 y x + 5 x d y)) (x^{2} y^{3})

= (x (4 y d x + 2 x d y) + y^{3} (3 x y + 5 x d y)) (x^{2} y^{3})

Apply the distributive law:

a (b + c) = ab + a c

a = (x^{2} y^{3}), b = x (4 y d x + 2 x d y), c = y^{3} (3 y x + 5 x d y)

= (x^{2} y^{3}) x (4 y d x + 2 x d y) + (x^{2} y^{3}) y^{3} (3 y x + 5 x d y)

= x (x^{2} y^{3}) (4 y d x + 2 x d y) + y^{3} (x^{2} y^{3}) (3 x y + 5 x d y)

Simplify

x (x^{2} y^{3}) (4 y d x + 2 x d y) + y^{3} (x^{2} y^{3}) (3 x y + 5 x d y) : 4 x^{3} y^{4} d x + 2 x^{4} y^{3} d y + 3 x^{3} y^{7} + 5 x^{3} y^{6} d y

= 4 x^{3} y^{4} d x + 2 x^{4} y^{3} d y + 3 x^{3} y^{7} + 5 x^{3} y^{6} d y

s cos (x) (1 + t a gx)

k (c + d - e)

((i + j) \times i) \times j

(x csc (\frac{y}{x}) - y) d x + x d y

- 2 (5 - 67)

What is expand (x(4ydx+2xdy)+y^3(3yx+5xdy))(x^2y^3) ?
The solution to expand (x(4ydx+2xdy)+y^3(3yx+5xdy))(x^2y^3) is 4x^3y^4dx+2x^4y^3dy+3x^3y^7+5x^3y^6dy