assuming x>0 ?

Can't x and y be elements of the Reals ?

Well seems i've messed up this... anyway

assume(n, natural);

evalb(sum(binomial(n, k)*x^(n-k)*y^k, k = 0 .. n) = (y+x)^n);

false

simplify(sum(binomial(n, k)*x^(n-k)*y^k, k = 0 .. n));

(y+x)^(n~)