Answer to Question #2834 in Algebra for munu

Question #2834

Factorize-
(x-y)[sup]3[/sup]+(y-z)[sup]3[/sup]+(z-x)[sup]3[/sup]+(x+y)[sup]3[/sup]

Expert's answer

(x-y)³ + (y-z)³ + (z-x)³+ (x+y)³ = x³ - y³ -3xy(x-y) + y³ - z³ -3 yz(y-z) +z³ - x³ - 3zx(z-x) + x³+y³ + 3xy(x+y) =
= x³ + y³ + 6xy² - 3y²z + 3yz² - 3z²x + 3zx²

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