<s>[INST] Find coefficient of $x^2$ Let $C$ be the coefficient of $x^2$ in the expansion of the product
$$(1-x)(1+2x)(1-3x) \cdots (1+14x)(1-15x)$$
Find: $\lvert C \rvert $
 [/INST] You may consider doing it manually. 
A term of $x^2$ arises from the product of two factors with the $1$s from the rest, so by multiplying all the pairs of coefficients we get our answer. 
Or, our answer is: $$|-1(2-3+4-5 \dots 14-15) + 2(-3+4-5-6\dots -13+14-15) \dots -13(14-15) +14(-15)|$$
$$=|-1(-7) + 2(6-15) - 3(-6) + 4(5-15) -5(-5) \dots -13(-1) +14(-15)|$$
$$=588$$
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