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use this relation to understand better,
( x − a ) ( x − b ) = x 2 + ( a − b ) x + a b
( x − a ) ( x − b ) ( x − c ) = x 3 − ( a + b + c ) x 2 + ( a b + b c + c a ) x − a b c
( x − a 1 ) ( x − a 2 ) ( x − a 3 ) . . . . . . . . ( x − a n ) = x n − ( a 1 + a 2 + a 3 + . . . . + a n ) x n − 1 + ( ∑ a 1 a 2 ) x n − 2 − . . . . . − ( a 1 a 2 . . . a n )
We can find that there are 49 terms in the question, from the AP- 2,4,6,....,98
Using the above relation,
The coefficient of x 4 8 will be-
− ( 2 + 4 + 6 + . . . . . . + 9 8 ) = − 2 4 5 0