Innings2
Create New Account

Sign in to Innings2

or

New Account     Reset Password     

Chapter 11: Algebraic Expressions

    Introduction

    Like and Unlike Terms

    Addition and Subtraction of Algebraic Expressions

    Multiplication of Algebraic Expressions

    Multiplication of a Monomial by a Monomial

    Multiplication of a Binomial or Trinomial by a Monomial

    Multiplication of a Binomial by a Binomial or Trinomial

    What is an Identity ?

    Some Important Identities

    Applications of Identities

    Geometric Verification of the Identities

    Exercise 11.1

    Exercise 11.2

    Exercise 11.3

    Exercise 11.4

    Exercise 11.5

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

Powered by Innings 2

Reset Progress

This will delete your progress and chat data for all chapters in this course, and cannot be undone!

Glossary

Select one of the keywords on the left…

Chapter 11: Algebraic Expressions > What is an Identity ?

What is an Identity ?

An identity is a mathematical equation that remains true for all possible values of its variable(s). Let's understand this with an example:

Consider the equation: (x+3)² = x² + 6x + 9

Let's verify this equation by checking it for different values of x:

For x = 1: LHS = (1+3)² = 4² =

RHS = 1² + 6(1) + 9 = + + 9 =

For x = -2: LHS = (-2+3)² = 1² =

RHS = (-2)² + 6(-2) + 9 = - + =

We can see that LHS = RHS for any value of x we choose. This makes the equation an identity.

To contrast this, let's look at an equation that is not an identity: x² - 1 = 0

This equation is only true for x = or x = -, but not for all values of x. Such an equation is called a conditional equation.

  • An identity is an equation that is true for all values of its variable(s)

  • A conditional equation is true only for specific values

  • We use the symbol '≡' to denote an identity (read as "is identically equal to")

This distinction between identities and regular equations is fundamental in algebra and helps us understand the universal nature of certain mathematical relationships.