Question

(C) x8 - 1 factorice it completely​

Answer 1

Step-by-step explanation:

GIven : x8−1

We can further write it as

x8−1=(x4)2−12

Based on the equation a2−b2=(a+b)(a−b)

We get,

x8−1=(x4+1)(x4−1)

x8−1=(x4+1)((x2)2−12)

x8−1=(x4+1)(x2+1)(x2−1)

So we get

x8−1=(x4+1)(x2+1)(x2−1)

By expanding the terms using the formula

We get,

x8−1=[(x2)2+12+2x2−2x2](x2−1)(x+1)(x−1)

On further simplification

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