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\[\frac{ x ^{36}-y ^{36} }{ (x ^{18}+y ^{18}) (x ^{9}+y ^{9}) }\]
a^2n - b^2n = (a^n + b^n) (a^n - b^n) try to apply this in the numerator
so we don't FOIL in this case?

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just add the common values? the x's and y's?
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FOIL method will be too long so you must try to factor the numerator and then cancel the common terms in the numerator nd denominator x^36-y^36 = (x^18-y^18)(x^18+y^18)
hmmmm okay.... so tell me if this is right
So after splitting the numerator like this ^ can u see any terms cancelling??
|dw:1439310575742:dw|
can you do that with the denominator?
No
but why not? Since they're multiply isnt it |dw:1439310745161:dw|
the denominator - (x^18+y^18)(x^9+y^9) =x^27 + (x^18)(y^9) + y^27 +(x^9)(y^18)
So you're saying the denominator must be FOILed right?
NOOOOOO i know what youre gonna say you're gonna say it's too long to FOIL but i'm just asking in general you cant add them like i asked previously because in these problems it has to be foiled right?
my method to solve the problem = we can write the numerator as - (x^36-y^36) = (x^18+y^18)(x^18-y^18) =(x^18+y^18)(x^9+y^9)(x^9-y^9) so now we plug this value of numerator in - (x^36-y^36)/[(x^18+y^18)(x^9+y^9)] so we have - [(x^18+y^18)(x^9+y^9)(x^9-y^9)]/[(x^18+y^18)(x^9+y^9)] after cancelling the common terms we have - x^9-y^9 as our answer
I know how to do the problem I just need you to confirm what I asked.
?

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