In order to evaluate and simplify algebraic expressions, we need to follow the order of operations (PEMDAS) and combine like terms.

Let’s look at an example:

Evaluate and simplify the expression 3x + 2y - 4x + 5y - 2z, when x = 2, y = 3, and z = 1.

First, we substitute the given values into the expression:

3(2) + 2(3) - 4(2) + 5(3) - 2(1)

Next, we simplify each term:

6 + 6 - 8 + 15 - 2

Now, we combine like terms:

6 - 8 + 6 + 15 - 2

-2 + 6 + 15 - 2

4 + 15 - 2

19 - 2

Finally, we get the simplified expression:

17