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rcmath eNotes educator| Certified Educator

The trick to this problem is to know what to multiply first. 
Difference if square rule states: `(x-y)(x+y)=(x^2-y^2)`

Keeping that in mind, we will work from left to right in order to apply this rule few times without having to do a lot of work.

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

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

`(x^4-y^4)(x^4+y^4)=`

`(x^8-y^8)`