What Have We Discussed ?

Algebraic expressions are formed from variables and constants. We use the operations of addition, subtraction, multiplication and division on the variables and constants to form expressions. For example: the expression 4xy + 7 is formed from the variables x and y and constants 4 and 7. The constant 4 and the variables x and y are multiplied to give the product 4xy and the constant 7 is added to this product to give the expression.

Expressions are made up of .

Terms are addedmultiplied to make an expression. For example, the addition of the terms 4xy and 7 gives the expression 4xy + 7.

A term is a productsum of factors.

The term 4xy in the expression 4xy + 7 is a product of factors x, y and 4. Factors containing variables are said to be algebraic factors.

The is the numerical factor in the term.

Sometimes anyone factor in a term is called the coefficient of the remaining part of the term.

Any expression with one or more terms is called a polynomial. Specifically a one term expression is called a ; a two-term expression is called a ; and a three-term expression is called a .

Terms which have the same algebraic factors are like terms. Terms which have different algebraic factors are unlike terms. Thus, terms 4xy and – 3xy are like terms; but terms 4xy and – 3x are not like terms.

In situations such as solving an equation and using a formula, we have to find the value of an expression. The value of the expression depends on the value of the variable from which the expression is formed. Thus, the value of 7x – 3 for x = 5 is 32, since 7(5) – 3 = 35 – 3 = .