Page 1 - LN-4-Standard Identities

SAI International School
Class VIII

Mathematics
Chapter 9 – Algebraic expressions & Identities
Lesson note -4
Subtopic: Standard Identities and Application

Application of identities

Identities
An identity is an equality which is true for every value of the variable but an equation is
true for only some of the values of the variables.

So an equation is not an identity.

2
Like, x = 1, is valid if x is 1 but is not true if x is 2.so it is an equation but not an identity.

Some of the Standard Identities
(a + b) = a + 2ab + b 2
2
2
2
2
(a - b) = a – 2ab + b 2
a – b = (a + b) (a - b)
2
2
2
(x + a) (x + b) = x + (a + b)x + ab
(a + b + c) = a + b + c + 2ab + 2bc + 2ca
2
2
2
2
These identities are useful in carrying out squares and products of algebraic
expressions. They give alternative methods to calculate products of numbers and so on.
Applying Identities
Example
(4x – 3y) 2
= (4x) – 2(4x) (3y) + (3y) 2
2
2
= 16x – 24xy + 9y 2
Example
Use the Identity (x + a) (x + b) = x + (a + b) x + ab to find the value of 501 × 502
2
Solution:
501 × 502

= (500 + 1) × (500 + 2)

= 500 + (1 + 2) × 500 + 1 × 2
2