5/9/13 Problems on Numbers Important Formulas - Aptitude Questions and Answers

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1. Some Basic Formulae:

i. (a + b)(a - b) = (a2 - b2)

ii. (a + b)2 = (a2 + b2 + 2ab)

iii. (a - b)2 = (a2 + b2 - 2ab)

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

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

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

vii. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)

viii. When a + b + c = 0, then a3 + b3 + c3 = 3abc.