Mechanical Vs Smart Appraoch

Algebra Level 2

Let S=(x1)4+4(x1)3+6(x1)2+4(x1)+1\displaystyle S={ \left( x-1 \right) }^{ 4 }+{ 4\left( x-1 \right) }^{ 3 }{ +6\left( x-1 \right) }^{ 2 }+4\left( x-1 \right) +1. Then S equals:

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