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Multiplication - Shortcuts

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  • Product of two numbers =Product of their H.C.F. and L.C.M.

    1. Multiplication By Distributive Law :

    1. a x (b + c) = a x b + a x c
    2. ax(b-c) = a x b-a x c.

    2. Multiplication of a Number By 5n

    :

    Put n zeros to the right of the multiplicand and divide the number so formed by 2n

    BASIC FORMULAE

    1. (a + b)2 = a2 + b2 + 2ab
    2. (a - b)2 = a2 + b2 - 2ab
    3. (a + b)2 - (a - b)2 = 4ab
    4. (a + b)2 + (a - b)2 = 2 (a2 + b2)
    5. (a2 - b2) = (a + b) (a - b)
    6. (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)
    7. (a3 + b3) = (a +b) (a2 - ab + b2)
    8. (a3 - b3) = (a - b) (a2 + ab + b2)
    9. (a3 + b3 + c3 -3abc) = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)
    10. If a + b + c = 0, then a3 + b3 + c3 = 3abc.

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