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Problems on Numbers - Important Formulae

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  1. Some Basic Formulae:
    1. (a + b)(a - b) = (a2 - b2)
    2. (a + b)2 = (a2 + b2 + 2ab)
    3. (a - b)2 = (a2 + b2 - 2ab)
    4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
    5. (a3 + b3) = (a + b)(a2 - ab + b2)
    6. (a3 - b3) = (a - b)(a2 + ab + b2)
    7. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
    8. When a + b + c = 0, then a3 + b3 + c3 = 3abc.
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