My 100 followers problem!

Algebra Level 4

Let \(P(x) : (x - 1)(x - 2)(x - 3) \dots\ (x - 50)\)

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

If \[P(x)Q(x) = a_{100}x^{100} + a_{99}x^{99} + \ldots\ + a_{1}x^1 + a_0,\] then compute \(a_{100} -a_{99} - a_{98} - a_{97}.\)

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