What is the difference between evaluation and simplification of an expression?

Answer 1

Evaluation is the process of finding the numerical value of an expression. For instance, suppose you wanted to know what x^3 was when x = 2. You would plug in 2 for x and get 2^3. This process is evaluation.

Simplifying an expression on the other hand doesn't necessarily involve finding any particular value. For instance, suppose you started with the expression (x^3)/(x^2) then recognized that the numerator and denominator share a common factor of x^2 and so rewrote the expression as x. This is simplification because you've put the expression into an equivalent form that may be easier or more useful to deal with, but you have not found a specific value.

You can also simplify numerical values -- for instance, 12/20 can be rewritten as 3/5. Often it's necessary to simplify a numerical expression after evaluating an algebraic one.