Question

i) x^8-1 factorise each of the following ​

Answer 1

Answer:

(x2+1+2x)(x2+1−2x)(x2+1)(x+1)(x−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

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

Using the formula we get

x8−1=(x2+1+2x)(x2+1−2x)(x2+1)(x+1)(x−1)