$x^{8} +98 x^{4}+1=(x^4+8x^2+1)^2-16x^2(x^2+1)^2$

That is strange, when I make your multiplication I get $x^8+34x^4+1$...

But \[\begin{array}{lll}x^{8}+98 x^{4}+1&=&(x^{4}+8x^{2}+1)^{2}-16x^{2}(x^{2}-1)^{2}\\&=& (x^{4}+4x^{3}+8x^{2}-4x+1)(x^{4}-4x^{3}+8x^{2}+4x+1)\end{array}\] does the job.