Question

Which of the following expressions are equivalent to 2/x^8-y^8? choose all that apply

A.2/(x^4-y^4)*1/(x^4+y^4)
B.2/(x^4)^2-(y^4)^2
C.2/(x4-y^4)*1/(x^4-y^4)
D.1/(x^4-y^4)*1/(x^4+y^4)

Answer 1

2/x^8-y^8 =2/(x^4-y^4)^2=2/(x^4-y^4) * 1/(x^4-y^4)

Answer 2

Option A and B are correct

`(2)/((x^4)^2-(y^4)^2)`and
`(2)/(x^4-y^4) * (1)/(x^4+y^4)`

Explanation:

Using the identity rule:

`x^2-y^2 = (x+y)(x-y)`

Given the expression:

`(2)/(x^8-y^8)`

We can write this as:

`(2)/((x^4)^2-(y^4)^2)`

Apply the identity rules:

`(2)/((x^4-y^4)(x^4+y^4))`

We can write this as:

`(2)/(x^4-y^4) * (1)/(x^4+y^4)`

Therefore, the expressions which is equivalent to
`(2)/(x^8-y^8)` are:
`(2)/((x^4)^2-(y^4)^2)` and
`(2)/(x^4-y^4) * (1)/(x^4+y^4)`