import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem algebra_3rootspoly_amdtamctambeqnasqmbpctapcbtdpasqmbpctapcbta (b c d a : ℂ) :
    (a - d) * (a - c) * (a - b) =
      -((a ^ 2 - (b + c) * a + c * b) * d) + (a ^ 2 - (b + c) * a + c * b) * a := by sorry