For LHS, basically you make all the possible "combos" for a term of xn+1.
From sasquatch's working,
and from the question,
a term of xn+1 may be obtained by x.xn, or x2.xn-1, x3.xn-2 etc, where
the coefficient of x from the first bracket in (1+x)n.(1+x)n, ie. (1+x)n is nC1, and that...