MathematicsEvaluate the following product without multiplying directly 77×79.

Evaluate the following product without multiplying directly 77×79.


  1. A
    6083
  2. B
    6073
  3. C
    6082
  4. D
    6012 

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    Solution:

    It is given  77×79.
    We know the formula that,
    x-ax-b=x2-a+bx+ab.
    Simplify given expression as,
    77×79=80-3×80-1  ....(1)       
    Applying the identity,
    x-ax-b=x2-a+bx+ab  in equation (1), where x = 80, a = -3 and b = -1, we get,
    80-380-1=802+((-3)+(-1))80+(-3)(-1) (80-3)(80-1)
    6400+(-3-1)80+(3) (80-3)(80-1) 6400+(-4)80+(3) (80-3)(80-1) 6400-320+3 (80-3)(80-1) 6400-317 (80-3)(80-1) 6083  77×79=6083.
    Therefore, option 1 is correct.
     
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