smc

Let $y=x-1$. Substitution results in $$S=y^4+4y^3+6y^2+4y+1$$ $$S=(y+1{)}^4$$ Substituting back results in $$S=x^4$$ The answer is $\boxed{x^4}$. This problem can also be solved by traditionally expanding and combining like terms (though it would take much longer).