Introduction to Chapter 12 - Algebraic Expressions

 Algebraic Expression

(VII CBSE Maths)

 A variable can take various values. Its value is not fixed. We use letters x, y, l, m, ... etc. to denote variables.  On the other hand, a constant has a fixed value. Examples of constants are: 4, 100, –17, etc.  We combine variables and constants to make algebraic expressions. For this, we use the operations of addition, subtraction, multiplication and division.

Factors and Terms in an Algebraic Expression

For instance,  the expression 4x + 5 is obtained from the variable x, first by multiplying x by the constant 4 and then adding the constant 5 to the product. Similarly, 10y – 20 is obtained by first multiplying y by 10 and then subtracting 20 from the product. 

We can also obtain expressions by combining variables with themselves or with other variables.  Look at how the following expressions are obtained: x2, 2y2, 3x2 – 5, xy, 4xy + 7 

 TERMS OF AN EXPRESSION

Consider the expression (4x + 5). In forming this expression, we first formed 4x separately as a product of 4 and x and then added 5 to it. 

Similarly consider the expression (3x2 + 7y). Here we first formed 3x2 separately as a product of 3, x and x. We then formed 7y separately as a product of 7 and y. Having formed 3x2 and 7y separately, we added them to get the expression.  Such parts of an expression which are formed separately first and then added are known as terms. 

Look at the expression (4x2 – 3xy). We say that it has two terms, 4x2 and –3xy. The term 4x2 is a product of 4, x and x, and the term (–3xy) is a product of (–3), x and y. 

Terms are added to form expressions. Just as the terms 4x and 5 are added to form the expression (4x + 5), the terms 4x2 and (–3xy) are added to give the expression (4x2 – 3xy). This is because 4x2 + (–3xy) = 4x2 – 3xy.

Note, the minus sign (–)  is included in the term. In the expression 4x2 –3xy, we took the term as (–3xy) and not as (3xy). That is why we do not need to say that terms are ‘added or subtracted’ to form an expression; just ‘added’ is enough.

Factors of a term :  The term 4x2 is a product of 4, x and x; we say that 4, x and x are the factors of the term 4x2. A term is a product of its factors. The term –3xy is a product of the factors –3, x and y.