For non-negative integers a and b, where a and b are both greater than or equal to 2, simplify the following:
\(\binom{a + b}{2} - \binom{a}{2} - \binom{b}{2}.\)
\(\binom{a + b}{2} - \binom{a}{2} - \binom{b}{2} = a + b + 1\)
