NCERT Book Class 7 Maths Chapter 10 Algebraic Expressions

160 MATHEMATICS

Chapter 10
Algebraic
Expressions

10.1 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 formu-
lating 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.
10.2 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.
The above expressions were obtained by combining variables with constants. 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
(i) The expression x2 is obtained by multiplying the variable x by itself;
x × x = x2
Just as 4 × 4 is written as 42, we write x × x = x2. It is commonly read as x squared.