SOLUTION: Simplify. (x^16-y^16)/(x^8-y^8)

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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