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.
A term of an algebraic expression is a constant, variable or a combination (product or quotient) of constants and variables. Two or more terms of an algebraic expression are separated from each other by addition (+), subtraction (–) or both signs.
A factor of a term is an exact divisor of the term. Factors containing variables are said to be algebraic factors.
The numerical factor of the term is said to be the numerical coefficient or coefficient of the term.
Terms with same literal coefficients, i.e., terms with same variables having same exponents are called like terms.
Terms with different literal coefficients or different exponents are called unlike terms.
An expression having one or more terms is called a polynomial. An expression having only one term is known as monomial. An expression which contains two unlike terms is called a binomial. An expression which contains three unlike terms is called a trinomial.
To add or subtract two or more like terms, we add or subtract the numeral coefficients of the given terms and form another like term with the sum or difference obtained as the numerical coefficient of the resulting term. The unlike terms cannot be added or subtracted the way like terms are added or subtracted.
While adding two algebraic expressions, their like terms are added and unlike terms remain as it is.
For solving an equation, the value of an expression is to be found. The value of the expression depends on the value of the variable from which the expression is formed.
Algebraic expressions are useful in writing the rules and formulae in mathematics in a general and compact form. For example: Area of Square = a x a = a2, where a = side of the square. If a natural number is denoted by n, then 2n is an even number and (2n + 1) an odd number.