Question

(x8-2) (x4-1)-x12+2x4

Answer 1

$(x^8-2)(x^4-1)-x^{12}+2x^4=x^{12}-x^8-2x^4+2-x^{12}+2x^4=\\\\=2-x^8=(\sqrt2)^2-(x^4)^2=(\sqrt2-x^4)(\sqrt2+x^4)=\\\\=(\sqrt[4]2-x^2)(\sqrt[4]2+x^2)(\sqrt2+x^4)=\\\\=(\sqrt[8]2-x)(\sqrt[8]2+x)(\sqrt[4]2-+x^2)(\sqrt2+x^4)$