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Chapter 1. Introduction. 1.1 Algebra. The word “algebra” means many things. The word dates back about 1200 years ago to part of the title of al-Khw¯arizm¯ı's 

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MATHEMATICAL FORMULAE. Algebra. 1. (a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab. 2. (a − b)2 = a2 − 2ab + b2; a2 + b2 = (a − b)2 + 2ab. 3. (a + b + c)2