(1998^2 - 1996^2)(1998^2 - 1995^2) ........1998^2
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(1997^2 - 1996^2) ( 1997^2 - 1995^2) .......1997^2
(1998 + 1996)(1998 - 1996) ( 1998 + 1995)(1998 - 1995) (1998 + 1994) (1998 - 1994).....1998^2
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(1997 + 1996) (1997 - 1996) (1997 + 1995)(1997 - 1995) (1997 + 1994)(1997 - 1994).....1997^2
[ (3994)(2)] [ (3993)(3) ] [(3992)(4) ].......[(1998)(1998)]
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[ (3993)(1)] [ (3992)(2)] [ (3991)(3)]..........[(1997)(1997)]
Note that each pair of products in the numerator sum to 3996 and each pair of of products in the numerator sum to 3994
After cancellation of like terms we are left with
3994 * ( 4) [(1998)(1998)]
_____ ..... _____________
( 3991) [ (1997)(1997)]
And....note that the sum of the non-cancelled terms in the middle fraction's numerator and denominator = 3995
This implies.....that after complete evaluation ( and cancellations), we will be left with
3994 * (1998)
______ =
(1997)
(2)(1997) * (1998)
_______________ =
(1997)
2 * 1998 =
3996