On the right hand side, distribute (x+y) in the other parenthesis and then compare the variables to the left hand side to figure out the factors:
(x+y)(ax2 + bxy + cy2)
ax3 + byx2 + cxy2 + ayx2 + bxy2 + cy3
Comparing to the left side. a and c must be 1.
And b has to be -1 so that all the other terms can cancel out.