Question
$(x - y) (x + y) (x^2 + y^2) (x^4+ y^4)$ is equal to:
✓
Answer
$(x - y)(x + y) = x^2 - y^2[$by identity ($a + b)(a - b) = a^2 - b^2]$
$(x^2 - y^2)(x^2 + y^2) = x^4 - y^4$
$(x^4 - y^4)(x^4 + y^4) = x^8 - y^8$
Now$,$
$(x - y)(x + y)(x^2 + y^2)(x^4 + y^4)$
$= (x^2 - y^2)(x^2 + y^2)(x^4 + y^4)$
$= (x^4 - y^4)(x^4 + y^4)$
$= x^8 - y^8$
$(x^2 - y^2)(x^2 + y^2) = x^4 - y^4$
$(x^4 - y^4)(x^4 + y^4) = x^8 - y^8$
Now$,$
$(x - y)(x + y)(x^2 + y^2)(x^4 + y^4)$
$= (x^2 - y^2)(x^2 + y^2)(x^4 + y^4)$
$= (x^4 - y^4)(x^4 + y^4)$
$= x^8 - y^8$
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