The square of the difference of two expressions is equal to the square of the first minus twice the product of the first and the second plus the square of the second.
Let us prove the formula from left to right, i.e. prove that:
The square of the expression is the expression mutiplied by itself:
Expand the brackets:
As the product remains the same by reordering its factors, then:
Collect like terms and multiply the elements:
As a result, we can derive:
Let us write in the form:
Apply this to the expression under consideration:
Factorize the common factors; and put -b outside the second bracket:
Factorize the expression (a-b):
As a result of transformations we have a product of the expression by itself, and it is the square of this expression:
Hence, we have proved that:
The Formula has been derived.