output formatting – How can I remove the negative sign to make sure the positive-signed term comes first?

I found the default dealing of the terms often display a negative sign at the beginning, including those beneath a square-root sign , which is a little bit annoying since for most cases, there exists at least one positive-signed term in the result and the negative sign can be adjusted by directly being moved backward after the positive-signed term or being multiplied into one difference term, swapping the two numbers in the difference term and thus avoiding a negative sign at the beginning. How can I remove the negative sign to make sure the term with positive sign comes first(if there is any)?

Example1:
-(a+b)(c-d)

Current result:
(-a - b) (c - d)

What I want:

(a+b)(d-c)

Example2:
Integrate(2 g y Sqrt(2 r y - y^2) (Rho), {y, 0, h}, Assumptions -> (r | h | g) (Element) PositiveReals && h <= 2 r) // FullSimply

Current Result:
ConditionalExpression( 1/3 g (Rho) (2 Sqrt(-h^5 (h - 2 r)) - r (Sqrt(-h^3 (h - 2 r)) + 3 Sqrt(-h (h - 2 r)) r) + 6 r^3 ArcCsc(Sqrt(2) Sqrt(r/h))), h < 2 r)

i.e.
$frac{1}{3} g rho left(2 sqrt{-h^5 (h-2 r)}-r left(sqrt{-h^3 (h-2 r)}+3 r sqrt{-h (h-2 r)}right)+6 r^3 text{arccsc}left(sqrt{2} sqrt{frac{r}{h}}right)right)text{ if }h<2 r$

The result I want:
ConditionalExpression( 1/3 g (Rho) (2 Sqrt(h^5 (2 r-h)) - r (Sqrt(h^3 (2 r-h)) + 3 Sqrt(h (2 r-h)) r) + 6 r^3 ArcCsc(Sqrt(2) Sqrt(r/h))), h < 2 r)

i.e.
$frac{1}{3} g rho left(2 sqrt{h^5 (2 r-h)}-r left(sqrt{h^3 (2 r-h)}+3 r sqrt{h (2 r-h)}right)+6 r^3 text{arccsc}left(sqrt{2} sqrt{frac{r}{h}}right)right)text{ if }h<2 r$

Example 3:

Dt(Log((Csc(x) - Cot(x))), x)

Current result:
(-Cot(x) Csc(x) + Csc(x)^2)/(-Cot(x) + Csc(x))

What I want:

(Csc(x)^2-Cot(x) Csc(x) )/(Csc(x)-Cot(x))

Example 4:
Dt(x ArcSin(x/2) + Sqrt(4 - x^2), x)

Current result:
-(x/Sqrt(4 - x^2)) + x/(2 Sqrt(1 - x^2/4)) + ArcSin(x/2)

What I want:

x/(2 Sqrt(1 - x^2/4))-(x/Sqrt(4 - x^2)) + ArcSin(x/2)

Example 5:
Integrate(1/(x^4 - a^4), x)

Current result:
Log(a - x)/(4 a^3)-(ArcTan(x/a)/(2 a^3)) - Log(a + x)/(4 a^3)