Polynomials

Questions
,
1

I get

(x+1/x)^3 = 1/x^3 + 3/x + 3 x + x^3

by Expand

Need to collect ALL POWERS of (x+1/x) and substitute for value (1 in this case)

x^3+1/x^3+3(x+1/x) = x^3+1/x^3+3

Thanks

2

Are you looking for a function to do this? I’m not exactly sure what this meant to do for a general case, but for your specific case I might write some code like this:

eqn = Expand[(x + 1/x)^3];

This gives us the expanded form you mentioned. Next we need to specify what powers of x we want to treat separately from the rest and pull them out of the equation:

pattern = _ x | _ Power[x, -1];
{matches, extra} = {Cases[eqn, pattern], Cases[eqn, Except@pattern]}

The tool we want to use to factor the number three out of the section that matches our pattern is FactorTerms. So FactorTerms[Plus @@ matches] Gives 3 (1/x + x):

targetFormat = Plus @@ extra + FactorTerms[Plus @@ matches]

This gives us the form you wanted for the equation and then we can subsitute that case of x+ 1/x for 1:

targetFormat /. (1/x + x) -> 1