My 100 followers problem!

Algebra Level 3

Let P(x):(x1)(x2)(x3) (x50)P(x) : (x - 1)(x - 2)(x - 3) \dots\ (x - 50)

Let Q(x):(x+1)(x+2)(x+3) (x+50)Q(x) : (x + 1)(x + 2)(x + 3) \dots\ (x + 50)

If P(x)Q(x)=a100x100+a99x99+ +a1x1+a0,P(x)Q(x) = a_{100}x^{100} + a_{99}x^{99} + \ldots\ + a_{1}x^1 + a_0, then compute a100a99a98a97.a_{100} -a_{99} - a_{98} - a_{97}.

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