Simplify: (x-y)(x+y) (x^2+y^2 ) (x^4+y^2 ) - Vidyadip

Question

Simplify:
$(x-y)(x+y)\left(x^2+y^2\right)\left(x^4+y^2\right)$

✓

Answer

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

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