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