Can highlight an expression in mathematica in an expansion?

Question

I ask mathematica to make an expansion of some expression. Is there a way to ask mathematica to highlight all terms that, say, goes by x^3 since it is really hard to find them? E.g.

Expand[(x + y) (x + z) (x + w)]

gives

w x^2 + x^3 + w x y + x^2 y + w x z + x^2 z + w y z + x y z

and the question is how can I highlight or isolate all terms that go as x^3?

Answer 1

One way could be using a Style.

Expand[(x + y) (x + z) (x + w)] /. {x^2 ->  
   Style[x^2, Red, Background -> LightBlue]}

Answer 2

Try this:

    expr = Expand[(x + y) (x + z) (x + w)];
rule[x_] := x -> Style[x, Background -> Yellow];

Then you may apply the rule to the expression as follows

expr /. rule[x^3]

with the effect

or

expr /. rule[x^2]

giving

but the most simple substitution

expr /. rule[x]

does not work, since it highlights all terms containing x. But this might be no problem for your aims.

Have fun!

Answer 3

Just an extension to Alexei Boulbitch's answer: if you want to highlight x, you can change the function to:

Clear[rule];
expr = Expand[(x + y) (x + z) (x + w)];
rule[x_] := {Power[x, y_] :> Power[x, y], 
  x :> Style[x, Background -> Yellow]}