Since multiplication is basically addition, why can't unlike terms in polynomials be added or subtracted, but they can be multiplied?
Thanks in advance for clarification.
Well, your basic problem is thinking that "multiplication is basically addition" and that "multiplication is addition". That is simply not true. We can think of multiplication as "repeated addition", as pickslides said, but since the number of times we repeat the addition is itself a variable, addition and multiplication cannot be expected to have the same properties.