Question

Which expression is equivalent to x^8-256

Answer 1

`\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)}`

Explanation:

`\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)`