Simplifying Cubic
What do we get after simplifying:
( x 4 + x 2 y 2 + y 4 ) ( x − y ) x 6 − y 6
Inspiration: Real Algebra 2
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3 solutions
Thanks for recommending my problem this is also a very nice one
I used the same solution
Have you tried Real Algebra (1)?
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I don't remember, do you have it's link?
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https://brilliant.org/problems/real-algebra/?ref_id=1590610
Nice problem! By the way, how do you cancel terms in LaTeX? Thanks!
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use \cancel{} and \bcancel{}
hey,mahdi please state that the x =!y
( x 4 + x 2 y 2 + y 4 ) ( x − y ) x 6 − y 6 = ( ( x 2 + y 2 ) 2 − x 2 y 2 ) ( x − y ) ( x 3 − y 3 ) ( x 3 + y 3 ) = ( x 2 + x y + y 2 ) ( x 2 − x y + y 2 ) ( x − y ) ( x − y ) ( x 2 + x y + y 2 ) ( x + y ) ( x 2 − x y + y 2 ) = x + y
I think you have a typo in the numerator of the first term. It’s x 6 − y 6
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Thanks, I have amended it
Multiply and divide by x+y we will directly get x+y
Let a = x 2 and b = y 2
( x 4 + x 2 y 2 + y 4 ) ( x − y ) x 6 − y 6 = ( a 2 + a b + b 2 ) ( x − y ) a 3 − b 3 = ( a 2 + a b + b 2 ) ( x − y ) ( a − b ) ( a 2 + a b + b 2 ) = x − y x 2 − y 2 = x − y ( x + y ) ( x − y ) = x + y