Question

Factorise x8-2374 +149 x 720​

Answer 1

Step-by-step explanation:

GIven : x

8

−1

We can further write it as

x

8

−1=(x

4

)

2

−1

2

Based on the equation a

2

−b

2

=(a+b)(a−b)

We get,

x

8

−1=(x

4

+1)(x

4

−1)

x

8

−1=(x

4

+1)((x

2

)

2

−1

2

)

x

8

−1=(x

4

+1)(x

2

+1)(x

2

−1)

So we get

x

8

−1=(x

4

+1)(x

2

+1)(x

2

−1)

By expanding the terms using the formula

We get,

x

8

−1=[(x

2

)

2

+1

2

+2x

2

−2x

2

](x

2

−1)(x+1)(x−1)

On further simplification

x

8

−1=[((x

2

)

2

+1

2

+2x

2

)−2x

2

](x

2

+1)(x+1)(x−1)

Using the formula we get

x

8

−1=(x

2

+1+

2

x)(x

2

+1−

2

x)(x

2

+1)(x+1)(x−1)