8.1. Find the value of the expression $\frac{\left(a^{2}+b^{2}\right)^{2}-c^{2}-4 a^{2} b^{2}}{a^{2}+c-b^{2}}$ for $a=2017, b=2016, c=2015$. Justify your result.
Answer: 2018. Solution. The numerator equals $a^{4}+2 a^{2} b^{2}+b^{4}-4 a^{2} b^{2}-c^{2}=\left(a^{2}-b^{2}\right)^{2}-c^{2}=$ $\left(a^{2}-b^{2}+c\right)\left(a^{2}-b^{2}-c\right)$, and after dividing by the denominator we get $a^{2}-b^{2}-c=$ $(a-b)(a+b)-c=2017+2016-2015=2018$.