Several blogs ago, I had suggested the use of a powerful fundamental algebraic identity:

.

Now, this identity becomes a basic applied tool in Algebra and Trigonometry and Number theory, perhaps.

A salient feature of mathematics is that mathematicians always try to generalize a technique or concept.

Can you generalize the above identity as follows (a proof is required please):

Let there be quantities a,b,c,d…then prove that

is divisible by and also find the quotient.

Please do send your questions, comments, suggestions …

More later…

Nalin Pithwa