`(1/2 xy - 1) . (x^{3} - 2x - 6)`
`= 1/2 xy . (x^{3} - 2x - 6) + (-1) . (x^{3} - 2x - 6)`
`= 1/2 xy . x^{3} + 1/2 xy . (-2) + 1/2 xy . (-6) + (-1) . x^{3} + (-1) . (-2x) + (-1) . (-6)`
`= 1/2 x^{4}y - x^{2}y - 3xy - x^{3} + 2x + 6`
`= 1/2 x^{4}y - x^{3} - x^{2}y - 3xy + 2x + 6`