Question

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

Answer 1

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

Explanation:

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

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`