a, [tex]x^8 + 4[/tex]
= [TEX]x^8 + 4x^4 + 4 - 4x^4[/TEX]
= [TEX](x^4 + 2)^2 - 4x^4[/TEX]
= [TEX](x^4 - 2x^2 + 2)(x^4 + 2x^2 + 2)[/TEX]
b, [TEX]64x^4 + 81[/TEX]
= [TEX]64x^4 + 144x^2 + 81 - 144x^2[/TEX]
= [TEX](8x^2 + 9)^2 - 144x^2[/TEX]
= [TEX](8x^2 + 12x + 9)(8x^2 - 12x + 9)[/TEX]