The coefficient of in the LHS is
The coefficient of in the RHS is
But the coefficients are the same, so we have the equality.
I have a question, which I've been pondering over for a few hours, and just can't seem to grasp it.
(m+n)C(3) = (m)C(3) + (m)C(2)*(n)C(1) + (m)C(1)*(n)C(2) + (n)C(3)
I've tried simplify the LHS down to (m+n)(m+n-1)(m+n-2)/3! But this didn't help, and I've tried simplify, and canceling down the RHS too, but I always end up with a huge expansion (18 terms ).
Could anyone lend a helping hand? Or some insight into the problem?