Question 1054348
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)