Algebraic expressions consist of variables and constants.
Operations such as addition, subtraction, multiplication and division are used 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.
Variable: Symbols which are used to represent or replace numbers. They are denoted as x, y, z, a, b, c…… and can take different numerical values. We generally use small letters to represent variables.
Constant: A symbol having a fixed numerical value. Example: 2, -10, etc.
Expressions are made up of terms. Terms are added to make an expression. For example, the addition of the terms 4xy and 7 gives the expression 4xy + 7.
A term is a product 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 coefficient is the numerical factor in the term. Sometimes anyone factor in a term is called the coefficient of the remaining part of the term.
Polynomial is any expression with one or more terms.
Monomials are single term expressions, binomials are two term expressions and trinomials are three term expressions.
Degree of polynomial is the highest power term in the polynomial.
Terms which have the same algebraic factors are like terms. Terms which have different algebraic factors are unlike terms. Thus, terms 18xy and – 2xy are like terms; but terms 18xy and – 22x are not like terms.
The sum (or difference) of two like terms is a like term with coefficient equal to the sum (or difference) of the coefficients of the two like terms. Thus, 8xy – 3xy = (8 – 3)xy, i.e., 5xy.
When we add two algebraic expressions, the like terms are added as given above; the unlike terms are left as they are. Thus, the sum of 4x2 + 5x and 2x + 3 is 4x2 + 7x + 3; the like terms 5x and 2x add to 7x; the unlike terms 4x2 and 3 are left as they are.
In situations such as solving an equation and using a formula, we have to find the value of an expression. The value of expression is found when we put value of variable in the expression. Thus, the value of 4x – 3 for x = 2 is 5, since 4(2) – 3 = 8 – 3 = 5.
Formulas are written in general form using algebraic expressions. For example
The area of rectangle = l x b, where l is the length and b is the breadth of the rectangle.
The general (nth) term of a number pattern (or a sequence) is an expression in n.
Thus, the nth term of the number pattern 11, 21, 31, 41, . . . is (10n + 1).
Number of diagonals drawn from one vertex of polygon of n sides are n-3.