Crossword Genius

Extremely happy and profitable promotion (4)

Ross

I believe the answer is:

hype

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'promotion' is the definition.
(I know that hype is a type of promotion)

'extremely happy and profitable' is the wordplay.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'and' is a charade indicator (letters next to each other).
'profitable' becomes 'pe' (I am not sure about this - if you are sure you should believe this answer much more).
'happy' with its middle removed is 'hy'.
'hy'+'pe'='HYPE'

Can you help me to learn more?

(Other definitions for hype that I've seen before include "Doer of dirty work" , "A promoter" , "Sensational publicity" , "Salesman's exaggeration" , "Ballyhoo" .)

I've seen this clue in The Times.
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