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Shortening Polynomials


Dear Mathgroupers,

Many thanks for all the replies I got for my previous requests.  I
have a feeling this may be trivial, but I often want to shorten
polynomials, after using Expand.  At the moment, I use the following
type of unwieldy expression:

t1 = a0 + a1 q + a2 q^2 ;
Expand[%^4] /. {q^3->0,q^4->0,q^5->0,q^6->0,q^7->0,q^8->0};

Is there a neater way to collect powers up to order m after
expanding a polynomial?

Thanks,
Stephen

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Stephen Corcoran,		email:	corcoran at stats.ox.ac.uk (internet)
Dept. of Statistics,			corcoran at uk.ac.ox.stats (janet)
University of Oxford,
1, South Parks Road		phone:  (0865) 272879
OXFORD, OX1 3TG			fax:	(0865) 272595
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