NCERT Book Class 9 Mathematics Chapter 4 Exploring Algebraic Identities

Exploring Algebraic
4 Identities

4.1 Introduction
In earlier chapters, you learnt about linear polynomials and how
they can be used to represent and solve real-life problems. You
also studied linear equations and discovered how they describe
relationships between quantities.
In this chapter, we will take the next step by exploring algebraic
identities. These are special mathematical rules that not only make
it easier to simplify complicated calculations but also help us work
efficiently with algebraic expressions.
Let us begin by exploring a few simple patterns.
Example 1: Consider any three consecutive square numbers. For
example, 1, 4, and 9. Add the smallest and the largest squares. Thus,
1 + 9 = 10. Then subtract twice the middle square from this sum. This
leads to 10 – (2 × 4) = 10 – 8 = 2.
Now try the same process with another set of three consecutive
square numbers. Say 9, 16, 25.

For example, consider the consecutive squares 25, 36, 49.
Applying the same rule we get (25 + 49) – (2 × 36) = 74 – 72 = 2.
Repeat this process with other sets of three consecutive square
numbers. The result always seems to be 2!
The pattern may look surprising, but soon we will uncover the
reason behind it using algebra.

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