Question

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

Answer 1

`\dbinom{2n}2=((2n!))/(2!(2n-2)!)=\frac{2n(2n-1)}2=n(2n-1)=2n^2-n`


`2\dbinom n2+n^2=2(n!)/(2!(n-2)!)+n^2=n(n-1)+n^2=2n^2-n`