+++(a−b)(a−c)(a−d)(x−b)(x−c)(x−d)(b−c)(b−d)(b−a)(x−c)(x−d)(x−a)(c−d)(c−a)(c−b)(x−d)(x−a)(x−b)(d−a)(d−b)(d−c)(x−a)(x−b)(x−c) = ?
Hint: An equation of nth degree with more than n roots is an identity. This is studied extensively in the wiki: The method of undetermined coefficients.