Most of the ways described can be performed syntax free with the context pannel

https://www.maplesoft.com/support/help/Maple/view.aspx?path=worksheet%2freference%2fcontextpanel

https://www.maplesoft.com/support/help/Maple/view.aspx?path=worksheet%2fexpressions%2fmanipulatecsm

combine(factor(expand(n*x^n - 2*n*x^(n - 1) + x^n)))

As an alternative to extracting and dissembling the RootOf expression with index=real[4] its possible in this case to substitute the solution for “a” (which comes with the RootOf expression for b) into the original expression expr

Download RootOf_index_real_solution_.mw

The condition all parameters are positive is not sufficient to decide on the sign of the roots since a[1] to a[3] can become negative or positive depending on the values of the parameters.

You have to provide relations between parameters (e.g. b>r) to determine ranges for a[1] to a[3] which then might enable you to determine ranges for the roots. Even then I have little hope that you will get a simple answer.

If I add a dot to expr=0  to the first command I get the same output.

solve({0 <~ (a, b), expr = 0.}, [a, b], allsolutions);
(solve(expr = 0., [a, b], useassumptions, allsolutions) assuming (0 <~ (a, b)));
solve({0 <~ (a, b), expr = 0.}, [a, b], allsolutions);

Edit:

In the attachment you can see for the exact solutions that

• only two solutions are identical
• the solution s2 is clearly different from all other solutions since there is no solution with a=sqrt(3)-1=0.73. It seems that the solutions with RootOf are not displayed.
• I am not really an expert with RootOf expressions

I hope someone more experienced can have a look at it.

solve_RootOf.mw (updated after edit)

To what I can see with printlevel:=100 simplify calls simplify,size in both cases

value remembered (in simplify): \`simplify/do\`(a*f(x)+b*f(x)+a*g(x)+1/(a*f(x)+b*f(x)+a*g(x)), size) -> a*f(x)+b*f(x)+a*g(x)+1/((a+b)*f(x)+a*g(x))

For me it looks like that simplify,size could do better on such expressions.

For your example it is possible to execute a Maple command within Flow

convert(1000*Unit('Omega'), units, Unit('`kΩ`'))

To preserve the value one (i.e. "1") in front of kOhm

convert(evalf(1000*Unit('Omega')), units, Unit('`kΩ`'))

Supported prefixes can be found here.

If you execute

expr:=(c[2]+x)^3+a; 
printlevel:=100;  
simplify(expr)

you can see that simplify/size is called nummerous times but only after simplify/normal has been called which expands expr to
x^3+3*x^2*c[2]+3*x*c[2]^2+c[2]^3+a

Then simplify/size is applied

--> enter \`simplify/size\`, args = x^3+3*x^2*c[2]+3*x*c[2]^2+c[2]^3+a

So, simplify tries to reduce the size of the above expression but not of the original.

Expanding with the normal command at the toplevel of the simpify logic seems to be a design descision.

Update: As someone who has never mastered algsubs, all I can say is that (as I read the algsubs documentation) it should have worked.  Maybe someone else can say why swapping sides was needed to make it work. I would be interested to learn.

Update2: From the algsubs help page: 

The function algsubs performs an algebraic substitution, replacing occurrences of a with b in the expression f.

I.e. lhs is replaced with rhs.

Download with_and_wo_algsubs.mw

If working with equations instead of assignments to names g and f is an option you could do

Download with_eqn.mw

You could insert a table like in the attached where the borders are set to none and the width of the first row sets the indent

Download Bullet.mw

I assume that "simplify" without options on this complex expression has too many cases to be examined by the underling algorithm.

Try alternatively

simplify(exprB, exp)

Download integration_with_units_reply.mw

The intersection of the two expressions is a surface
 

plot3d(1/5*b^2 - 1/5*b*x - 1/5*x^2, b = -4 .. 4, x = -4 .. 4)

intersectplot plots "intersection of 2 surfaces in 3-D" which is a curve

Try this

plot3d([b, b^2/4, -b/2], b = -4 .. 4, thickness = 5, color = red, style = line)