Give an algebraic proof that:
2n choose 2 = 2*(n choose 2) + n^2

Question

Give an algebraic proof that:
2n choose 2 = 2*(n choose 2) + n^2

anonymous · Answer

i think all you need is to write out what both sides actually are

anonymous · Answer

on the other hand, being algebra challenged today, either it is wrong or i am missing something

anonymous · Answer

that's right, just not sure about the expansion

anonymous · Answer

lhs is $2n(2n-1)=4n^2-2n$ 
rhs is $2n(n-1)+n^2=2n^2-2n+n^2=3n^2-2n$ so either they are not the same or i a need to go get more coffee

zarkon · Answer

you didn't divide by 2

anonymous · Answer

ho ho ho

anonymous · Answer

guess that would help wouldn't it?

zarkon · Answer

you do need to hit the coffee  :)

anonymous · Answer

yeah i am really messing up today
i blame the heat
which is in fact why i am indoors on a saturday

anonymous · Answer

$\binom{2n}{2}=\frac{2n(2n-1)}{2}=n(2n-1)$
$2\binom{n}{2}+n^2=\frac{2n(n-1)}{2}+n^2$ now algebra