How do you expand $(c+1/c)^4$ ?

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Answer 1 · 2016-07-22T18:27:27

$=c^4 + 4c^2 + 6 + 4/c^2 + 1/c^4$

We can use Pascal's triangle or binomial theorem. As the exponent is low we shall just use the triangle.

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Exponent is 4 so use the fourth line. We will have:

$1*(c)^4*(1/c)^0 + 4*(c)^3*(1/c)^1 + 6*(c)^2*(1/c)^2 + 4*(c)^1*(1/c)^3 + 1*(c)^0*(1/c)^4$

$=c^4 + 4c^2 + 6 + 4/c^2 + 1/c^4$

How do you expand (c+1/c)^4(c+1/c)^4?