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Remarkable identities

- Square of an addition: (a + b)2 = a2 + b2 + 2ab
(a + b)2 = (a + b)·(a + b) = a2 + ab + ba + b2 =
= a2 + b2 + 2ab


- Square of a subtraction: (a - b)2 = a2 + b2 - 2ab
(a - b)2 = (a - b)·(a - b) = a2 - ab - ba + b2 =
= a2 + b2 - 2ab


- Addition multiplied by subtraction: (a + b)·(a – b) = a2 - b2
(a + b)·(a – b) = a2 - ab + ba - b2 = a2 – b2