1. Introduction to algebraic expressions

Various definitions and concepts
    Literals : The letters which are used to represent numbers are called literal numbers or literals. In 2xy, x & y are the literals.
    Literal numbers obey all the rules (and signs) of addition, subtraction, multiplication and division of numbers along with the properties of these operations. a × b = ab, 2 × a = 2a, 1 × a = a, x × 3 = 3x and a × a × a × ......× 15 times = a¹⁵. 
    In a⁵, 5 is called the index or exponent and a is called the base.

    Constant :  A term of the expression having no literal factor is called a constant term.

    (i)     In the binomial expression 5x + 7, the constant term is 7. In short, a symbol having a fixed numerical value is called a constant.

Variable : A symbol which takes various numerical values is called a variable.

Algebraic expression : A combination of constants and variables connected by the signs of fundamental operations of addition, subtraction, multiplication and division is called an algebraic expression.

Chapter -12

Algebraic expressions

Introduction to algebraic expressions

Algebra is the branch of mathematics that deals with the methods of finding the unknown values by using the variables and constants in the algebraic expression.
Algebraic expressions:
Combine variables and constants using the mathematical operations addition and subtraction to construct algebraic expressions.
Terms are either variables, numbers or variables multiplied together with numbers. An algebraic operation like addition and subtraction separates terms.

Variable: A variable is a symbol for an unknown value. It is usually denoted in a letter like x, y, a, b.

The number of terms: The total number of terms is known as the number of terms of a given expression.

Constant: A number which stands alone without any variables is known as constant.

Coefficient: A co-efficient can either be a numerical factor or an algebraic factor or product of both that is a number used to multiply a variable.

E.g. Kathir went to a shop to buy chocolate. He gave to shop keeper ₹50 and the shopkeeper gave him 10 chocolates.Now can you find the cost of one chocolate?

Let x be the cost of one chocolate. Then,

 x ×10=50x = 5010 = 5.

Therefore the cost of one chocolate is ₹5.