When it comes to evaluating algebraic expressions we first must understand what an expression is. An expression is made up of terms separated by addition and subtraction operations. There are no equal signs because it is not an equation. A term can include a variable such as y, a variable and a number such as 3y, or just a number, 3. Terms also have variables with exponents 3y². Evaluating expression involves substituting a number in place of the variable. How do we know that the number is? We are given this information. For example, evaluate the expression 3 + y, when y is 6. We cannot add 3 + y without having a value of y. Y is 6, so we plug 6 in for y and simplify. 3 + 6 and we get 9. Now let us evaluate 3y. The operation here is multiplication, 3 times y. We plug 6 in for y, and chug our way through the problem. 3 times 6 = 18. We have evaluated 3 + y and 3y or 3 times y, when we let y = 6. Sometimes we have to evaluate expressions that involve several variables. Nothing changes; we follow the same process of plug and chug to evaluate the expression. For example, evaluate y - z, when y = 2 and z = - 1. We plug in -2 for y and -1 in for z and chug or work our way through the problem.
2 – ( -1) remember we are subtracting z and z is negative 1, so we subtract negative 1.
2 + 1 = 3
Evaluate the expression 3y² when y = 5. This has a variable and the exponent only applies to y, not to the 3. We are therefore only raising y to the second power. 3 *5². Order of operations calls for doing the exponent part first, we have 5² = 5 * 5 which is 25. Now we multiply this result by 3. 3 * 25 = 75. We have evaluated the expression 3y² when y is equal to 5.
Evaluating expressions can only occur when we know what the values of the variables are. Just plug in the value given to you and work your way through the rest of the problem. 