Answer:
[tex]\large\boxed{x^8-256=(x^4+16)(x^4-16)=(x^4+16)(x^2+4)(x^2-4)}\\\boxed{=(x^4+16)(x^2+4)(x+2)(x-2)}[/tex]
Step-by-step explanation:
[tex]\text{use}\ a^2-b^2=(a-b)(a+b)\ \text{and}\ (a^n)^m=a^{nm}\\\\x^8-256=x^{4\cdot2}-16^2=(x^4)^2-16^2=(x^4+16)(x^4-16)\\\\=(x^4+16)(x^{2\cdot2}-4^2)=(x^4+16)[(x^2)^2-4^2]=(x^4+16)(x^2+4)(x^2-4)\\\\=(x^4+16)(x^2+4)(x^2-2^2)=(x^4+16)(x^2+4)(x+2)(x-2)[/tex]
