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Which expression is equivalent to x^8-256

User Qwertzuiop
by
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1 Answer

4 votes

Answer:


\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)

User Laurent Debricon
by
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