// minds behind maths
Al-Khwarizmi
c. 780–850 CE · Algebra, arithmetic, astronomy
Muhammad ibn Musa al-Khwarizmi was a Persian polymath at the House of Wisdom in Baghdad during the Islamic Golden Age. His treatise Al-Jabr (The Compendious Book on Calculation by Completion and Balancing), written between 813 and 833, gave the first systematic solution of linear and quadratic equations and is the source of the word 'algebra' (from al-jabr). He solved quadratics by completing the square, with geometric justifications — the same square-and-rectangle reasoning behind the square identities such as (a+b)² in this section. The word 'algorithm' also derives from the Latinised form of his name.
Source: Wikipedia — Muhammad ibn Musa al-Khwarizmi
Formulas that trace back to Al-Khwarizmi
Square of (a+b−c)
(a+b-c)² = a²+b²+c²+2ab-2bc-2ca
Square of (a−b+c)
(a-b+c)² = a²+b²+c²-2ab-2bc+2ca
Square of (a−b−c)
(a-b-c)² = a²+b²+c²-2ab-2ca+2bc
Square of a Difference (a−b)²
(a-b)² = a² - 2ab + b²
Square of a Linear Trinomial (ax+by+c)²
(ax+by+c)² = a²x² + b²y² + c² + 2abxy + 2bcy + 2cax
Square of a Sum (a+b)²
(a+b)² = a² + 2ab + b²
Square of a Trinomial (a+b+c)²
(a+b+c)² = a²+b²+c²+2ab+2bc+2ca