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Square of a difference: `(a - b)^2`

The Formula

(a - b)2 = a2 + b2 - 2ab

Working forwards - Expansion

For example, the expression (4x - y)2 can be expanded as follows:
= (4x)2 + (y)2 - 2(4x)(y)
= 16x2 + y2 - 8xy

Working backwards - Factorization

For example, the expression x2 + 81y2 - 18xy can be factored as follows:
x2 + (9y)2 - 2(x)(9y)
On comparing it with a2 + b2 - 2ab
(x - 9y)2
.. which is the factored form.