What is expand-(x+2(ux))^2(xdu+udx) ?

The solution to expand-(x+2(ux))^2(xdu+udx) is -x^3du-4x^3udu-4x^3u^2du-x^2udx-4x^2u^2dx-4x^2u^3dx

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expand-(x+2(ux))^2(xdu+udx)

expand

- (x + 2 (ux))^{2} (x d u + u d x)

- x^{3} d u - 4 x^{3} u d u - 4 x^{3} u^{2} d u - x^{2} u d x - 4 x^{2} u^{2} d x - 4 x^{2} u^{3} d x

Solution steps

- (x + 2 (ux))^{2} (x d u + u d x)

= - (x + 2 (xu))^{2} (x d u + u d x)

Apply the distributive law:

a (b + c) = ab + a c

a = - (x + 2 (ux))^{2}, b = x d u, c = u d x

= - (x + 2 (ux))^{2} x d u + (- (x + 2 (ux))^{2}) u d x

Apply minus-plus rules

+ (- a) = - a

= - x (x + 2 (xu))^{2} d u - u (x + 2 (xu))^{2} d x

Simplify

- x (x + 2 (xu))^{2} d u - u (x + 2 (xu))^{2} d x : - x^{3} d u - 4 x^{3} u d u - 4 x^{3} u^{2} d u - x^{2} u d x - 4 x^{2} u^{2} d x - 4 x^{2} u^{3} d x

= - x^{3} d u - 4 x^{3} u d u - 4 x^{3} u^{2} d u - x^{2} u d x - 4 x^{2} u^{2} d x - 4 x^{2} u^{3} d x

(168 - 6 π x) (π x)

30 c m^{2} \cdot (x - 5) e (x + 2)

\frac{( x + 1 )}{x ( x ^{2} + 1 )}

\frac{4 π ( 3 r ^{2} + 3 h r + h ^{2} )}{3}

\frac{6 x}{( x - 3 ) ( x + 2 )}

What is expand-(x+2(ux))^2(xdu+udx) ?
The solution to expand-(x+2(ux))^2(xdu+udx) is -x^3du-4x^3udu-4x^3u^2du-x^2udx-4x^2u^2dx-4x^2u^3dx