1961 AHSME Problems/Problem 5

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Let $S=(x-1)^4+4(x-1)^3+6(x-1)^2+4(x-1)+1$. Then S equals:

(A) $(x-2)^4$ (B) $(x-1)^4$ (C) $x^4$ (D) $(x+1)^4$ (E) $x^4+1$