What is expand ((ux)-x)(udx+xdy) ?

The solution to expand ((ux)-x)(udx+xdy) is u^2xdx+ux^2dy-uxdx-x^2dy

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expand ((ux)-x)(udx+xdy)

expand

((ux) - x) (u d x + x d y)

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

Solution steps

((ux) - x) (u d x + x d y)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = (ux), b = - x, c = u d x, d = x d y

= (ux) u d x + (ux) x d y + (- x) u d x + (- x) x d y

Apply minus-plus rules

+ (- a) = - a

= u (ux) d x + x (ux) d y - ux d x - xx d y

Simplify

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

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

\frac{b}{( x ^{2} ( x + a ) )}

\frac{2 ( x ^{2} - 9 )}{x - 4}

\frac{6 a x}{( x + 2 ) ^{6}}

\frac{( 2 x - 7 ) ( 2 x + 7 )}{4}

(4 x) (5 x)

What is expand ((ux)-x)(udx+xdy) ?
The solution to expand ((ux)-x)(udx+xdy) is u^2xdx+ux^2dy-uxdx-x^2dy