Algebraic Formulae for competitive exams

                               Now I am presenting some algebraic formulae, which are very commonly used and very useful for some special simplification questions.

·         (a+b)² = a² + b² + 2ab                      ---------------------  (Equation no. 1)

·         (a-b)² = a² + b² - 2ab                        ---------------------  (Equation no. 2).

From Equation 1 & 2

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

·         (a+b)² - (a-b)² = 4ab                         ---------------------  (Equation no. 3)

From Equation 3

·         (a+b)² = (a-b)² + 4ab

·         (a-b)² =  (a+b)² - 4ab

Other Formulae

·         a² - b² = (a+b) (a-b)

·         (a+b)³ = a³ + b³ + 3ab (a+b) = a³ + 3a²b + 3ab² + b³

·         (a-b)³ = a³ - b³ - 3ab (a-b) = a³ - 3a²b + 3ab² - b³

·         (a³ + b³) = (a+b) (a² + b² - ab)

·         (a³ - b³) = (a-b) (a² + b² + ab)

·         (a+ b+ c)² = a² + b² + c² + 2 (ab + bc + ca) = a² + b² + c² + 2ab + 2bc + 2ca

·         a³ + b³ + c³ – 3abc = (a +b +c) (a² + b² + c² – ab – bc – ca)

                                    =  (a+b +c) [(a-b)² + (b-c)² + (c-a)²] 

if  a+ b+ c = 0

then  a³ + b³ + c³ = 3abc