Atrisinājums

Izmantojot saīsinātās reizināšanas formulas \((a-b)(a+b)=a^{2}-b^{2}\) un \(a^{2} \pm 2ab+b^{2}=(a \pm b)^{2}\), iegūstam

\(\left(x^{2}-2x+1\right)\left(x^{4}+1\right)^{2}\left(x^{2}+2x+1\right)\left(x^{4}+2x^{2}+1\right)=(x-1)^{2}\left(x^{4}+1\right)^{2}(x+1)^{2}\left(x^{2}+1\right)^{2}=\)
\(=((x-1)(x+1))^{2}\left(x^{2}+1\right)^{2}\left(x^{4}+1\right)^{2}=\left(x^{2}-1\right)^{2}\left(x^{2}+1\right)^{2}\left(x^{4}+1\right)^{2}=\)
\(=\left(x^{4}-1\right)^{2}\left(x^{4}+1\right)^{2}=\left(x^{8}-1\right)^{2}\)