An algebraic expression is one that contains one or more variables. To evaluate an algebraic expression means to replace the variable of variables in the expression with given numbered values and then simplify the resulting numerical expression.
On type of algebraic expression, in which the terms are all monomials, is called a polynomial. The four fundamental operations can be performed using essentially the same ideas. The commutative, associative, and distributive properties provide the basis for rearranging, regrouping, and combining similar terms in the addition and subtraction of polynomial expressions. To add polynomials, simply combine like terms. To subtract polynomials, simply add the opposite of the second polynomial to the first and combine liker terms. The final resulting polynomial in each case should be written in decreasing order according to the power of the variable. Either a vertical or horizontal format can be used for either operation. For example we can combine each of the following expressions using the indicated operations in vertical or horizontal format.