Mother of Multiplication!

use this relation to understand better,

$(x-a)(x-b) = x^2 + (a-b)x + ab$

$(x-a)(x-b)(x-c) = x^3 - (a+b+c)x^2 + (ab+bc+ca)x -abc$

$(x-{ a }_{ 1 })(x-{ a }_{ 2 })(x-{ a }_{ 3 })........(x-{ a }_{ n })=x^{ n }-({ a }_{ 1 }+{ a }_{ 2 }+{ a }_{ 3 }+....+{ a }_{ n })x^{ n-1 }+(\sum { { a }_{ 1 }{ a }_{ 2 } } ){ x }^{ n-2 }-.....-({ a }_{ 1 }{ a }_{ 2 }...{ a }_{ n })$

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 $x^{48}$ will be-

$-(2+4+6+......+98) = \boxed{-2450}$

there are 49 terms,, you must jump 48 brackets atleast to get x^(48) , after that you have to jump to constant term of the remaining bracket,, this way u can leave any one bracket and choose x from other brackets in 49 ways,, each giving u every constant term as the coefficient ,, so just sum em up,, and add a negative sign as there are odd number of terms