How many terms are in the simplified expression?

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Question from Anu, a student:

The expression (x+y+z)^2006 + (x-y-z)^2006 is simplified by expanding it and combining like terms.
How many terms are in the simplified expression?

I've spent hours on this. pls help!!!
Also, is answering these questions a paid job for you
or is it volunteer work?
I'd like to join an ask and answer site for math, (when I grow up)
How does one go about doing that?

Anu,

Note first that you don't need to actually compute trinomial coefficients. The coefficients will be zero if and only if the total power of y and z in the term (equivalently that of x) is odd.

So: how many triples (a,b,c) are there in which a+b+c is 2006 and a is odd?

Try substituting some smaller [even] numbers for 2006 and looking for a pattern. Arranging them in a triangle may help:

[400]		310		[220]		130		[040]
	301		[211]		121		(etc)

Good Hunting!
RD

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