Question

Factorise the following : x^6-1

Answer 1

Answer:

There are two methods for the same.

Step-by-step explanation:

a)

x^6 - 1

= (x^3)^2 - 1

= (x^3 + 1)(x^3 - 1)

= (x+1)(x^2 - x + 1)(x-1)(x^2 + x +1)

= (x+1)(x-1)(x^2 - x +1)(x^2 + x + 1)

 

b)

x^6 - 1

= (x^2)^3 - 1

= (x^2 - 1)(x^4 + x^2 + 1)

= (x+1)(x-1)(x^4+2x^2+1 - x^2)

= (x+1)(x-1)[(x^2+1)^2 - x^2)

= (x+1)(x-1)(x^2-x+1)(x^2+x+1)

Answer 2

(X^3)2-(1)^2

(X^3+1) (X^3-1)

(X+1) (X2-X+1) (X-1) (X^2+X+1)