replacement - Replacing a sum of expressions

I have an equation which Mathematica solves but gives a huge output. However I notice in this output that the same expression occurs many times. Namely:

$E=864 a^6 - 432 a^4 b^2 + 54 a^2 b^4 - b^6 + 54 b^4 x^2$

where $a,b,c$ are constants. However this expression can appear in the form $-E$, $E^2$, $\sqrt{E}$, $4E$, ...

I'm struggling to tell Mathematica to make the replacement

$(864 a^6 - 432 a^4 b^2 + 54 a^2 b^4 - b^6 + 54 b^4 x^2) \space \to \space E$

wherever it appears.

All the ways I've tried (I'm not that handy with Mathematica I note) don't change output. Any ideas?

Answer

You must carefully define all desired / expected replacement cases. For example:

poly = 864 a^6 - 432 a^4 b^2 + 54 a^2 b^4 - b^6 + 54 b^4 x^2;

Clear[rep]

rep[p_] := p /. p :> p[[0]]@B

rep[Power[p_, n_]] := p /. p :> Power[B, n]
rep[Times[n_, p_]] := p /. p :> n B

rep[poly]

B

rep[Log@poly]

Log[B]

rep[1/poly]

1 / B

rep[poly*2]

2 B

list = {poly, Log@poly, poly^2, 1/poly};

rep /@ list

{B, Log[B], B^2, 1/B}

I feel there should be easier solutions using the Hold..., Unevaluated, Inactive family. However, I can't find them.