Share

# Standard Identities

#### 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 [00:05:27]
S
0%

S