**Question:**

Verify the identity:

let us observe first that each of the fifth degree expression is just a quadratic in two variables x and y. Let us say the above identity to be verified is:

**Method I:**

**Use binomial expansion. It is a very longish tedious method. **

**Method II:**

**Factorize each of the quadratic expressions** **using quadratic formula method (what is known in India as Sridhar Acharya’s method):**

*Now fill in the above details.*

You will conclude very happily that :

The above identity is transformed to :

You will find that and

Hence, it is verified that the given identity .** QED. **

Regards,

Nalin Pithwa.