CBSE Class 8CBSE
Share
Notifications

View all notifications

Standard Identities

Login
Create free account


      Forgot password?

notes

Now study the three identiies which are very useful in our work. 
These identities are obtained by multiplying a binomial by another binomial.
Let us first consider the product `(a + b)^2 = (a + b) (a + b)` 
= a(a + b) + b (a + b) 
= `a^2 + ab + ba + b^2` 
= `a^2 + 2ab + b^2`            (since ab = ba)
Thus ,  `(a + b)^2 = a^2 + 2ab + b^2`                  (I)

⦁ we consider `(a – b)^2 = (a – b) (a – b) 
= a (a – b) – b (a – b)
= `a^2 – ab – ba + b^2 = a^2 – 2ab + b^2`
or `(a – b)^2 = a^2 – 2ab + b^2`              (II)   

⦁ Finally, consider (a + b) (a – b). 
We have (a + b) (a – b) = a (a – b) + b (a – b) 
= `a^2 – ab + ba – b^2  = a^2 – b^2 `         (since ab = ba) 
or `(a + b) (a – b) = a^2 – b^2`                  (III)
The identities (I), (II) and (III) are known as standard identities.

Shaalaa.com | Standard Identities

Shaalaa.com


Next video


Shaalaa.com


Standard Identities [00:05:27]
S
Series 1: playing of 1
0%


S
View in app×