Question
Simplify:
$ (x-y)(x+y)\left(x^2+y^2\right)\left(x^4+y^4\right) $
$ (x-y)(x+y)\left(x^2+y^2\right)\left(x^4+y^4\right) $
✓
Answer
To simplify, we will proceed as follows:
$ (x-y)(x+y)\left(x^2+y^2\right)\left(x^4+y^4\right) $
$ =\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left[\because(a+b)(a-b)=a^2-b^2\right] $
$ =\left(x^4-y^4\right)\left(x^4+y^4\right) $
$ =x^8-x^8 $
$ (x-y)(x+y)\left(x^2+y^2\right)\left(x^4+y^4\right) $
$ =\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left[\because(a+b)(a-b)=a^2-b^2\right] $
$ =\left(x^4-y^4\right)\left(x^4+y^4\right) $
$ =x^8-x^8 $
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