Final answer:
To simplify the expression (a+b) - (a) - (b) with non-negative integers a and b where a≥2 and b≥2, subtract a from (a+b) to get b and subtract b to end with 0. The provided extra information is not necessary for this straightforward arithmetic problem.
Step-by-step explanation:
To address the problem of simplifying the expression (a+b) - (a) - (b) given that a and b are non-negative integers where a≥2 and b≥2, we need to apply basic arithmetic principles. The original expression can be simplified by recognizing that subtracting a number by itself results in zero. Therefore, when we subtract a from (a+b), we are left with b, and subsequently subtracting b from b also results in zero. This leaves us with the simplified result of the expression which is 0.
The additional information provided regarding the substitution of values for variables and the binomial theorem appears to be irrelevant to the particular question being asked. Thus, the final simplified version of the original algebraic expression is simply 0.
The expression simplifies to zero. Alternative approaches, such as substituting values into complex equations or utilizing series expansions, would not be beneficial in this context. All that's required is the fundamental property of addition that assures us A+B = B+ A. This commutative property ensures that terms can be rearranged and combined or cancelled out straightforwardly, leading to an uncomplicated and clear solution.