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A list of formulae is given below. These formulae will help a lot to work out some problems.

· (a + b)^2 = a^2 + 2 a b + b ^2 = (a –b)^2 + 4 a b

· (a - b)^2 = a^2 - 2 a b + b ^2 = (a +b)^2 - 4 a b

· (a + b) (a – b) = a^2 – b^2

· a^2 + b^2 = (a + b)^2 – 2 a b = (a – b) ^2 + 2 a b

· (a + b)^2 + (a – b) ^2 = 2 (a^2 + b^2)

· (a + b) ^2 – (a – b) ^2 = 2 (a^2 + b^2)

· (a + b) ^2 + (a – b) ^2 = 4 a b

· (a + b)^3 = a^3 + 3 a^2 b + 3 a b^2 + b^3 = a^3 + b^3 + 3 a b (a + b)

· (a - b)^3 = a^3 - 3 a^2 b + 3 a b^2 - b^3 = a^3 - b^3 - 3 a b (a - b)

· (a + b) (a^2 – ab + b^2 ) = a^3 + b^3 = (a + b) ^3 – 3 a b (a + b)

· (a – b) (a^2 + ab + b^2) = a^3 – b^3 = (a – b)^3 + 3ab (a –b).