Eg:

Consider (x-1)(x-2)(x-3)

 

Now expanding it we get x³-(1+2+3)x²+(1*2+2*3+3*1)x-6

 

Similarly when we expand  (x-1)(x-2).......(x-100)

 

We get x¹⁰⁰ -(1+2+3....100)x⁹⁹+(Sum of product of all first 100 integers taken two at a time)x⁹⁸+................