# Not So Big!

Algebra Level 3

$$$\begin{split} & \dfrac{(x-b)(x-c)(x-d)}{(a-b)(a-c)(a-d)} \\+ & \dfrac{(x-c)(x-d)(x-a)}{(b-c)(b-d)(b-a)} \\ +& \dfrac{(x-d)(x-a)(x-b)}{(c-d)(c-a)(c-b)} \\ +& \dfrac{(x-a)(x-b)(x-c)}{(d-a)(d-b)(d-c)} \end{split}$$ ~=~?$

Hint: An equation of $$n^ \text{th}$$ degree with more than $$n$$ roots is an identity. This is studied extensively in the wiki: The method of undetermined coefficients.

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