Question

Which expression is equivalent to x^8-256

Answer 1

Answer:

$\large\boxed{x^8-256=(x^4+16)(x^2+4)(x+2)(x-2)}$

Step-by-step explanation:

$x^8-256\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=x^{(4)(2)}-16^2=(x^4)^2-16^2\qquad\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=(x^4+16)(x^4-16)=(x^4+16)(x^{(2)(2)}-4^2)\\\\=(x^4+16)\bigg((x^2)^2-4^2\bigg)=(x^4+16)(x^2+4)(x^2-4)\\\\=(x^4+16)(x^2+4)(x^2-2^2)\\\\=(x^4+16)(x^2+4)(x+2)(x-2)$