Question

factorise the term  x^8- y^8 

Answer 1

x^8-y^8
⇒(x^4)^2-(y^4)^2
⇒(x^4+y^4)(x^4-y^4)
⇒(x^4+y^4)[(x^2)^2-(y^2)^2]
⇒(x^4+y^4)(x^2+y^2)(x^2-y^2)
⇒(x^4+y^4)(x^2+y^2)(x+y)(x-y)

Answer 2

x^8-y^8
we can write x^8 as (x^4)^2
⇒(x^4)^2-(y^4)^2
It is in the form of a^2-b^2=(a+b)(a-b)
Here we have a=x^4 and b=y^4
⇒(x^4+y^4)(x^4-y^4)
⇒(x^4+y^4)[(x^2)^2-(y^2)^2]
Again it is in the form of a^2-b^2=(a+b)(a-b)
Here a=x^2 and b=y^2
⇒(x^4+y^4)(x^2+y^2)(x^2-y^2)
Applying A^2-b^2 formulae for x^2-y^2
Formulae for it is ((a-b)(a+b))
Here a=x and b=y
⇒(x^4+y^4)(x^2+y^2)(x+y)(x-y)