Question

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

Answer 1

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

Answer 2

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

Answer 3

that's right, just not sure about the expansion

Answer 4

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

Answer 5

you didn't divide by 2

Answer 6

ho ho ho

Answer 7

guess that would help wouldn't it?

Answer 8

you do need to hit the coffee :)

Answer 9

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

Answer 10

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