Question 1054348: Simplify.
(x^16-y^16)/(x^8-y^8)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x^16 - y^16 = (x^8)^2 - (y^8)^2
your equation becomes:
((x^8)^2 - (y^8)^2) / (x^8 - y^8)
since a^2 - b^2 = (a - b) * (a + b), we can make a = x^8 and b = y^8 and your expression will become:
((x^8 - y^8) * (x^8 + y^8)) / (x^8 - y^8)
the (x^8 - y^8) in the numerator and denominator cancel out and you are left with:
(x^8 + y^8).
that's your answer.
you can confirm the solution is correct by assuming a random value for x and a different random value for y and evaluating the original equation and then the final solution to see that they yield the same answer.
i used x = 5 and y = 3 and i got 397186 for both expressions.
i evaluated:
(x^16 - y^16) / (x^8 - y^8)
and i evaluated:
(x^8 + y^8)
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