NCERT Class 7 Maths Algebraic Expressions

Algebraic Expressions

12.1 INTRODUCTION

We have already come across simple algebraic expressions like x + 3, y – 5, 4x + 5, 10y – 5 and so on. In Class VI, we have seen how these expressions are useful in formulating puzzles and problems. We have also seen examples of several expressions in the chapter on simple equations.

Expressions are a central concept in algebra. This Chapter is devoted to algebraic expressions. When you have studied this Chapter, you will know how algebraic expressions are formed, how they can be combined, how we can find their values and how they can be used.

12.2 HOW ARE EXPRESSIONS FORMED?

We now know very well what a variable is. We use letters x, y, l, m, ... etc. to denote variables. A variable can take various values. Its value is not fixed. 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. We have already come across expressions like 4x + 5, 10y – 20. 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. 

 12.3 TERMS OF AN EXPRESSION

We shall now put in a systematic form what we have learnt above about how expressions are formed. For this purpose, we need to understand what terms of an expression and their factors are. 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.

 Coefficients

We have learnt how to write a term as a product of factors. One of these factors may be numerical and the others algebraic (i.e., they contain variables). The numerical factor is said to be the numerical coefficient or simply the coefficient of the term. It is also said to be the coefficient of the rest of the term (which is obviously the product of algebraic factors of the term). Thus in 5xy, 5 is the coefficient of the term. It is also the coefficient of xy. In the term 10xyz, 10 is the coefficient of xyz, in the term –7x²y², –7 is the coefficient of x²y^2.

When the coefficient of a term is +1, it is usually omitted. For example, 1x is written as x; 1 x²y² is written as x²y² and so on. Also, the coefficient (–1) is indicated only by the minus sign. Thus (–1) x is written as – x; (–1) x² y ² is written as – x² y² and so on.

Sometimes, the word ‘coefficient’ is used in a more general way. Thus we say that in the term 5xy, 5 is the coefficient of xy, x is the coefficient of 5y and y is the coefficient of 5x. In 10xy², 10 is the coefficient of xy2, x is the coefficient of 10y² and y² is the coefficient of 10x. Thus, in this more general way, a coefficient may be either a numerical factor or an algebraic factor or a product of two or more factors. It is said to be the coefficient of the product of the remaining factors.

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