Expand and equations

[soegaard]

Description

Expand lacks a rule for equations.

I expected Expand[eq1==eq2] to give Expand[eq1]==Expand[eq2].
Instead the original input is returned.

How to Reproduce

Enter: Expand[(x-1)*(x^2+1)==0]

Expected behavior

From WolframScript:

In[66]:= Expand[(x-1)*(x^2+1)==0]                                                        

                   2    3
Out[66]= -1 + x - x  + x  == 0

[axkr]

This is probably incomplete, but I think that the following functions:

Apart
Collect
ComplexExpand
Expand
ExpandAll
ExpandDenominator
ExpandNumerator
ExpToTrig
Factor
FactorSquareFree
FactorTerms
FunctionExpand
PowerExpand
Together
ToRadicals
TrigExpand
TrigReduce 
TrigToExp

Can be threaded other (nested) expressions with the following heads:

And
Or
Nand
Nor
Not
Implies
Equivalent
Equal
Unequal
Greater
GreaterEqual
Less
LessEqual
Xor

[rocky]

Conceptually, adding a rewrite rule is easy.

@soegaard As a workaround, perhaps you can come up with such a rewrite rule, suggest that, and use this in the interim.

When I look at the current Expand[] Python evaluation code, it could use an overhaul. So for myself, I would not contemplate expanding Expand until the internal code overhaul is done.