MATHEMATICS · Multi-part · AoPS · Mathematics · Special Factorizations · Special Factorizations
Problem
Let (a−b)2 denote the square of a difference.
(i) Rewrite (a−b)2 as a product of two identical binomials.
(ii) Expand the product obtained in part (i) and simplify it completely.
(iii) Hence or otherwise, establish the general identity for (a−b)2 in terms of a and b.
(iv) Verify the identity for a=9 and b=4 by computing both sides separately.