Question #2834
Factorize-
(x-y)[sup]3[/sup]+(y-z)[sup]3[/sup]+(z-x)[sup]3[/sup]+(x+y)[sup]3[/sup]
(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
= x3 + y3 + 6xy2 - 3y2z + 3yz2 - 3z2x + 3zx2
